Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to...Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.展开更多
In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In...In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.展开更多
In the present paper, we give some sufficient conditions for the commutativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.
Denote a semisimple Banach algebra with an identity e by A.This paper studies the Fredholm,Weyl and Browder spectral theories in a semisimple Banach algebra,and meanwhile considers the properties of the Fredholm eleme...Denote a semisimple Banach algebra with an identity e by A.This paper studies the Fredholm,Weyl and Browder spectral theories in a semisimple Banach algebra,and meanwhile considers the properties of the Fredholm element,the Weyl element and the Browder element.Further,for a∈A,we give the Weyl’s theorem and the Browder’s theorem for a,and characterize necessary and sufficient conditions that both a and f(a)satisfy the Weyl’s theorem or the Browder’s theorem,where f is a complex-valued function analytic on a neighborhood ofσ(a).In addition,the perturbations of the Weyl’s theorem and the Browder’s theorem are investigated.展开更多
Ⅰ. INTRODUCTION Since Berry’s discovery of the geometric phase in quantum adiabatic evolution, there has been increased interest in this holonomy phenomenon referred to as Berry phase. Aharonov and Anandan removed t...Ⅰ. INTRODUCTION Since Berry’s discovery of the geometric phase in quantum adiabatic evolution, there has been increased interest in this holonomy phenomenon referred to as Berry phase. Aharonov and Anandan removed the adiabatic condition and studied the geometric phase (AA phase) for any cyclic evolution. AA phase and Berry phase have been verified in展开更多
Ⅰ. DEFINITIONS AND SOME KNOWN RESULTSDefinition 1.1. Let (M, g) be a pseudo-Riemannian manifold and I be a paracomplex structure on M (the definition of paracomplex structure can be found in [1] and [2]). If the
Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G-variety. Assume that both G, X as well as the G-action on X are defined over real numbers.Then G（R） acts on X（R） with finite...Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G-variety. Assume that both G, X as well as the G-action on X are defined over real numbers.Then G（R） acts on X（R） with finitely many orbits. We describe these orbits in combinatorial terms using Galois cohomology, thus providing a patch to a result of Borel and Ji.展开更多
In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hale...In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.展开更多
For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order...For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order to obtain faster speed we modify the algorithm to compute the irreducible characters.展开更多
For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all...For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.展开更多
Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of rel...Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.展开更多
In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the...In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups.Only even quantizations were considered there.In this paper,these results are generalized to the case of general quantizations with arbitrary periods.The key step is to introduce an enhanced version of the(truncated)period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth sym-plectic variety X,with values in the space of Picard Lie algebroid over X.As an application,we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.展开更多
At present, Berry’s topological phase factor and the studies of its relevant problem have drawn considerable attention . It concerns the theoretical analysis of chiral anomaly, etc., which is also experimentally conf...At present, Berry’s topological phase factor and the studies of its relevant problem have drawn considerable attention . It concerns the theoretical analysis of chiral anomaly, etc., which is also experimentally confirmed. In general, the explicit determination of the展开更多
A polynomial p in a polynomial algebra over a field is called a test polynomial if any endomorphism of the polynomial algebra that fixes p is an automorphism. some classes of new test polynomials recognizing nonlinear...A polynomial p in a polynomial algebra over a field is called a test polynomial if any endomorphism of the polynomial algebra that fixes p is an automorphism. some classes of new test polynomials recognizing nonlinear automorphisms of polynomial algebras are given. In the odd prime characteristic case, test polynomials recognizing non-semisimple automorphisms are also constructed.展开更多
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups （G-groups）. In this paper we establish a decomposition theorem for irreduc...Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups （G-groups）. In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.展开更多
We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2...We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR（S1） and EndR（S2） are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer Kaplansky if and only if so is the class of simple R-modules.展开更多
In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. I...In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities
文摘Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.
基金The NSF (10961014) of Chinathe NSF (S2011010003681) of Guangdong Province+3 种基金the Science and Technology Projects (2010B010600039) of Guangdong Provincethe Excellent Youth Talent Foundation (2012SQRL115ZD) of Anhui Provincethe University Natural Science Project (KJ2012B133) of Anhui Provincethe NSF (2007LZ01) of Fuyang Normal College
文摘In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.
基金The Youth Science Foundation of Northeast Normal University (111494027) and the NNSF (10271076) of China.
文摘In the present paper, we give some sufficient conditions for the commutativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.
文摘Denote a semisimple Banach algebra with an identity e by A.This paper studies the Fredholm,Weyl and Browder spectral theories in a semisimple Banach algebra,and meanwhile considers the properties of the Fredholm element,the Weyl element and the Browder element.Further,for a∈A,we give the Weyl’s theorem and the Browder’s theorem for a,and characterize necessary and sufficient conditions that both a and f(a)satisfy the Weyl’s theorem or the Browder’s theorem,where f is a complex-valued function analytic on a neighborhood ofσ(a).In addition,the perturbations of the Weyl’s theorem and the Browder’s theorem are investigated.
基金Project supported by the Foundation for Ph. D. Training Programme of China and Zhejiang Provincial Natural Science Foundation of China
文摘Ⅰ. INTRODUCTION Since Berry’s discovery of the geometric phase in quantum adiabatic evolution, there has been increased interest in this holonomy phenomenon referred to as Berry phase. Aharonov and Anandan removed the adiabatic condition and studied the geometric phase (AA phase) for any cyclic evolution. AA phase and Berry phase have been verified in
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. DEFINITIONS AND SOME KNOWN RESULTSDefinition 1.1. Let (M, g) be a pseudo-Riemannian manifold and I be a paracomplex structure on M (the definition of paracomplex structure can be found in [1] and [2]). If the
基金partially supported by the Russian Foundation for Basic Research(Grant No.16-01-00818)
文摘Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G-variety. Assume that both G, X as well as the G-action on X are defined over real numbers.Then G（R） acts on X（R） with finitely many orbits. We describe these orbits in combinatorial terms using Galois cohomology, thus providing a patch to a result of Borel and Ji.
文摘In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.
文摘For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order to obtain faster speed we modify the algorithm to compute the irreducible characters.
文摘For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.
基金The Fundation of Key Research Program (02021029) and the NSF (2004kj352) of Anhui Province, China.
文摘Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.
基金Supported by China NSFC grants(Grant Nos.12001453 and 12131018)Fundamental Research Funds for the Central Universities(Grant Nos.20720200067 and 20720200071)。
文摘In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups.Only even quantizations were considered there.In this paper,these results are generalized to the case of general quantizations with arbitrary periods.The key step is to introduce an enhanced version of the(truncated)period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth sym-plectic variety X,with values in the space of Picard Lie algebroid over X.As an application,we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.
基金Project supported by the National Natural Science Foundation of China.
文摘At present, Berry’s topological phase factor and the studies of its relevant problem have drawn considerable attention . It concerns the theoretical analysis of chiral anomaly, etc., which is also experimentally confirmed. In general, the explicit determination of the
基金Project supported by the National Natural Science Foundation of China (Grant No. 19631100)University of Hong Kong RGC Fundable Grant 344/024/0004.
文摘A polynomial p in a polynomial algebra over a field is called a test polynomial if any endomorphism of the polynomial algebra that fixes p is an automorphism. some classes of new test polynomials recognizing nonlinear automorphisms of polynomial algebras are given. In the odd prime characteristic case, test polynomials recognizing non-semisimple automorphisms are also constructed.
文摘Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups （G-groups）. In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.
文摘We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR（S1） and EndR（S2） are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer Kaplansky if and only if so is the class of simple R-modules.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10271081)a Fund from Educational Department of Beijing(Grant No.2002KJ-100).
基金both The Research Affairs (Research Project No.850709)The Center of Excellence for Mathematics of the University of Isfahan
文摘In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.
