In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-her...In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.展开更多
This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classificati...This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras,or equivalently cofree pointed coalgebras,and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras.We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.展开更多
基金the Foundation of Zhangzhou Normal University (No.SK05012)
文摘In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.
基金supported by National Natural Science Foundation of China(Grant No. 10601052)Natural Science Foundation of Shandong Province(Grant No.2009ZRA01128)the Independent Innovation Foundation of Shandong University(Grant No.2010TS021)
文摘This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras,or equivalently cofree pointed coalgebras,and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras.We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.
