In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automor...In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.展开更多
In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary charact...In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, ...A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.展开更多
The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO' are proved to be invariant under automorphisms of SHO'. The proof involves the investigation of the ad-nilpotent elements of the even...The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO' are proved to be invariant under automorphisms of SHO'. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. A property of automorphisms of these Lie superalgebras can be established, and an intrinsic characterization of SHO' can be obtained.展开更多
We construct coherent states associated with the Lie superalgebra OSP(1. 2) with the aid of two SU(2) coherent states and discuss their properties in detail. We also evaluate the matrix elements of the OSP(1, 2) gener...We construct coherent states associated with the Lie superalgebra OSP(1. 2) with the aid of two SU(2) coherent states and discuss their properties in detail. We also evaluate the matrix elements of the OSP(1, 2) generators in the coherent-state representation and give a realization for the OSP(1, 2) generators in the coherent state space.展开更多
In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecodin...In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.展开更多
Let R be a commutative ring with identity 1. The relations between the ideals of Lie superalgebra P(n) and the ideals of R are discussed by studying the basis, center and order ideal of P(n). All ideals of P(n) ...Let R be a commutative ring with identity 1. The relations between the ideals of Lie superalgebra P(n) and the ideals of R are discussed by studying the basis, center and order ideal of P(n). All ideals of P(n) are proved to be minimal and standard.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.
We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the ...We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation展开更多
Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.
In this paper, the derivation algebra of Lie superalgebra H of Cartan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following: DerFH =...In this paper, the derivation algebra of Lie superalgebra H of Cartan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following: DerFH = adH(H + Fh) ⊕ {(adDi)pt | i = 1,2,··· ,m, t = 1,2,··· ,ti -1} .展开更多
Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.
Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p>2.In this paper,all the super-biderivations of L are studied.By means of weight space ...Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p>2.In this paper,all the super-biderivations of L are studied.By means of weight space decompositions with respect to a suitable torus and the standard Z-grading structures of L,we show that the super-symmetric superbiderivations of L are zero.Generalizing a result on the skewsymmetric biderivation of Lie algebras to the super case,we find that all the superbiderivations of L are inner.As applications,the linear supercommuting maps and the supercommutative post-Lie superalgebra structures on L are described.展开更多
In this paper,all symmetric super-biderivations of some Lie superalgebras are determined.As an application,commutative post-Lie super algebra structures on these Lie super algebras are also obtained.
In this note, the compatible left-symmetric superalgebra structures on an infinite-dimensional Lie superalgebra with some natural grading conditions are completely determined. The results of earlier work on left-symme...In this note, the compatible left-symmetric superalgebra structures on an infinite-dimensional Lie superalgebra with some natural grading conditions are completely determined. The results of earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures.展开更多
We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0(Ln,m) and Dery(Ln,m). B...We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0(Ln,m) and Dery(Ln,m). By computing a maximal torus on each Ln,m, we show that Ln,m are completable nilpotent Lie superalgebras. We also view Ln,m as Lie algebras, prove that Ln,m are of maximal rank, and show that Ln,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.展开更多
In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 + A2 +… +An, then Фp(L) = Фp(A1) +Фp(A2) +…+Фp(An), where each Ai is...In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 + A2 +… +An, then Фp(L) = Фp(A1) +Фp(A2) +…+Фp(An), where each Ai is a p-ideal of L. We then obtain two results: F(L) = Ф(L) = J(L) = L if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.展开更多
基金Supported by Youth Science Foundation of Northeast Normal University (111494027) National Natural Science Foundation of China (10271076)
文摘In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.
文摘In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金Project supported by the Science Foundation of the Educational Department of Shandong Province of China (Grant No.J07YH01)
文摘A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.
基金the Science Foundation of Harbin Normal University(KM2007-11)
文摘The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO' are proved to be invariant under automorphisms of SHO'. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. A property of automorphisms of these Lie superalgebras can be established, and an intrinsic characterization of SHO' can be obtained.
文摘We construct coherent states associated with the Lie superalgebra OSP(1. 2) with the aid of two SU(2) coherent states and discuss their properties in detail. We also evaluate the matrix elements of the OSP(1, 2) generators in the coherent-state representation and give a realization for the OSP(1, 2) generators in the coherent state space.
文摘In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.
文摘Let R be a commutative ring with identity 1. The relations between the ideals of Lie superalgebra P(n) and the ideals of R are discussed by studying the basis, center and order ideal of P(n). All ideals of P(n) are proved to be minimal and standard.
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We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation
基金the Fundamental Research Fund(2572018BC15)for the Central Universitiesthe NSF(11171055)of China
文摘Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.
基金Supported by the Natural Science Foundation of the Henan Institute of Science and Technology(06057)
文摘In this paper, the derivation algebra of Lie superalgebra H of Cartan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following: DerFH = adH(H + Fh) ⊕ {(adDi)pt | i = 1,2,··· ,m, t = 1,2,··· ,ti -1} .
文摘Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.
基金supported by NSF of China(12061029)and NSF of Heilongjiang Province(LH2022A019)supported by NSF of China(12061029)NSF of Hainan Province(120RC587).
文摘Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p>2.In this paper,all the super-biderivations of L are studied.By means of weight space decompositions with respect to a suitable torus and the standard Z-grading structures of L,we show that the super-symmetric superbiderivations of L are zero.Generalizing a result on the skewsymmetric biderivation of Lie algebras to the super case,we find that all the superbiderivations of L are inner.As applications,the linear supercommuting maps and the supercommutative post-Lie superalgebra structures on L are described.
基金Supported by NNSF(Grant Nos.12071405,11971315)Xinjiang Uygur Autonomous Region graduate scientific research innovation project(Grant No.XJ2021G021)。
文摘In this paper,all symmetric super-biderivations of some Lie superalgebras are determined.As an application,commutative post-Lie super algebra structures on these Lie super algebras are also obtained.
文摘In this note, the compatible left-symmetric superalgebra structures on an infinite-dimensional Lie superalgebra with some natural grading conditions are completely determined. The results of earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures.
文摘We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0(Ln,m) and Dery(Ln,m). By computing a maximal torus on each Ln,m, we show that Ln,m are completable nilpotent Lie superalgebras. We also view Ln,m as Lie algebras, prove that Ln,m are of maximal rank, and show that Ln,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.
基金Supported by National Natural Science Foundation of China (Grant No. 10271076)
文摘In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 + A2 +… +An, then Фp(L) = Фp(A1) +Фp(A2) +…+Фp(An), where each Ai is a p-ideal of L. We then obtain two results: F(L) = Ф(L) = J(L) = L if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.