Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-iso...Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix.展开更多
The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter gr...The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.展开更多
In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras. This approach also allows us to calculate the structure constants of multiplicat...In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras. This approach also allows us to calculate the structure constants of multiplication over the Grothendieck ring of the sequence.展开更多
In the present paper we describe a class of ep-Auslander-Yoneda algebras over K[χ]/（χ-n） in terms of quivers with relations, and prove that they are actually cellular algebras in the sense of Graham and Lehrer.
Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n...Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n matrices over R for any positive integer n.We show that Sn(φ,R)■M_(n)(R)is a separable Frobenius extension.If R is commutative,then Sn(φ,R)is a cellular algebra over the invariant subring R^(φ)of R.展开更多
基金This research work was supported by CFKSTIP(Grant No.704004)the Doctor Program Foundation(Grant No.20040027002),Ministry of Education of Chinapartially by National Natural Science Foundation of China(Grant No.103331030).
文摘Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix.
文摘The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.
文摘In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras. This approach also allows us to calculate the structure constants of multiplication over the Grothendieck ring of the sequence.
文摘In the present paper we describe a class of ep-Auslander-Yoneda algebras over K[χ]/（χ-n） in terms of quivers with relations, and prove that they are actually cellular algebras in the sense of Graham and Lehrer.
基金supported by Beijing Nova Program(Z181100006218010)by Research Ability Improvement Program of BUCEA(Grant No.X22026).
文摘Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n matrices over R for any positive integer n.We show that Sn(φ,R)■M_(n)(R)is a separable Frobenius extension.If R is commutative,then Sn(φ,R)is a cellular algebra over the invariant subring R^(φ)of R.
