Construction of semisimple category over generalized Yetter-Drinfeld modules

Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.

LOCAL AUTOMORPHISMS OF SEMISIMPLE ALGEBRAS AND GROUP ALGEBRAS

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.

Some Characterizations of Strongly Semisimple Ordered Semigroups

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.

On Restricted Lie Superalgebras with Semisimple Elements

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.

Hereditary Radicals and Strongly Semisimple Radicals in Normal Classes of Algebras

Puczylowski established the general theory of radicals of the class of objects called algebras. In this paper, we make use of the method of lattice theory to characterize the general hereditary radicals and general strongly semisimple radicals and investigate some properties of them in normal classes of algebras. This extends some known studies on the theory of radicals of various algebraic strutures.

A CLASS OF HOMOGENEOUS SEMISIMPLE SPACES

The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where G is a real simple Lie Group, W∈ g, C(W) 0 is the identity component of the centralizer C(W) of W in G .

The Weyl’s Theorem and Its Perturbations in Semisimple Banach Algebra

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.

TIME EVOLUTION AND AHARONOV-ANANDAN PHASE FOR SYSTEM WITH DYNAMICAL SEMISIMPLE LIE ALGEBRA

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

THE PARAKHLER METRICS ON SEMISIMPLE HOMOGENEOUS MANIFOLDS

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

Orbits of Real Semisimple Lie Groups on Real Loci of Complex Symmetric Spaces

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.

A Note on the Supersemiprime Rings and Supersemiprime Radical

In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .

Multiplicative Jordan Decomposition in Integral Group Ring of Group K_8×C_5

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.

（Inco） Projective Modules of Relatively Hereditary Torsion Theroy

In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco） τ-projective module and study their properties. When r is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a（inco） semisimple ring and satisfies（inco） condition.

Irreducible Representations of Algebraic Group <i>SL</i>(6,<i>K</i>) in char<i>K</i>=3

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.

On Ellipsoids Attached to Root Systems

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.

Some Rings Characterized by Modules

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A RELATION AMONG ASSOCIATIVE ALGEBRAS,BIALGEBRAS AND SEMIGROUP ALGEBRAS

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Semisimplicity of u-Quasi-Hopf Algebra

The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional projective H-module P such that dimu P is invertible.

Homological Dimensions and Semisimplicity of Relative Hopf Modules

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.

The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits

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.