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
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 proje...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.展开更多
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 st...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.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
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.
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
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 ...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 .展开更多
Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full m...Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k（X） of function algebra on a finite set X are considered.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
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.
文摘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.
文摘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.
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.
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
文摘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 .
基金supported by the National Natural Science Foundation of China(No.10731070)
文摘Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k（X） of function algebra on a finite set X are considered.
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
