This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applic...This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.展开更多
In this paper,we investigate the presentation for little q-Schur algebra u_(k)(3.5)at odd roots.The Poincaré-Birkhoff-Witt(PBW)basis of u_(k)(3.5)is obtained through the basis of q-Schur algebra U(3.5).Then we pr...In this paper,we investigate the presentation for little q-Schur algebra u_(k)(3.5)at odd roots.The Poincaré-Birkhoff-Witt(PBW)basis of u_(k)(3.5)is obtained through the basis of q-Schur algebra U(3.5).Then we present a new set for generators and relations for u_(k)(3.5)by PBW basis.展开更多
We develop and study the generalization of rational Schur algebras to the super setting.Similar to the classical case,this provides a new method for studying rational supermodules of the general linear supergroup GL(m...We develop and study the generalization of rational Schur algebras to the super setting.Similar to the classical case,this provides a new method for studying rational supermodules of the general linear supergroup GL(m|n).Furthermore,we establish a Schur-Weyl duality result for rational Schur superalgebras and conclude that under certain conditions these objects will be semisimple.展开更多
Let uk （2, r） be a little q-Schur algebra over k, where k is a field containing an ι＇-th primitive root ε of 1 with ι＇〉 4 even, the author constructs a certain monomial base for little q-Schur algebra uk （2...Let uk （2, r） be a little q-Schur algebra over k, where k is a field containing an ι＇-th primitive root ε of 1 with ι＇〉 4 even, the author constructs a certain monomial base for little q-Schur algebra uk （2, r）.展开更多
The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochsch...The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ:P → PAP. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations.展开更多
This paper is devoted to present some properties of the c-nilpotent multiplier M（c） （L） and some features of c-central extensions of a （finite dimensional） Lie algebra L.Moreover, we give the structure of all c-...This paper is devoted to present some properties of the c-nilpotent multiplier M（c） （L） and some features of c-central extensions of a （finite dimensional） Lie algebra L.Moreover, we give the structure of all c-covers of Lie algebras whose c-nilpotent multipliers have the Hopfian property.展开更多
In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKH...In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKHrpqsllll创串C, defined by: A(ei, ej, ek, es)=ijksa, where the (aijks)s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions rpqsllll哪?(( is not a Banach algebra under schur product.展开更多
In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.
For a partition λ and a prime p,we prove a necessary and sufficient condition for there to exist a composition δ such that δ can be obtained from λ after rearrangement and no partial sums of δ are divisible by p....For a partition λ and a prime p,we prove a necessary and sufficient condition for there to exist a composition δ such that δ can be obtained from λ after rearrangement and no partial sums of δ are divisible by p.To demonstrate why we are interested in the question,we compute some signed p-Kostka numbers.展开更多
Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimen...Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then ] induces a full embedding from ￡（△） to eAe-mod which preserves Ext-groups up to certain degrees, where ￡（△） denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq（n,r） with n≥r and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras.展开更多
基金supported by a 2017 University of New South Wales Science Goldstar Grant(Jie Du)the Simons Foundation(Grant Nos. #359360(Brian Parshall) and #359363 (Leonard Scott))
文摘This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.
基金Supported by the Natural Research Project of Yichang(A23-2-026)。
文摘In this paper,we investigate the presentation for little q-Schur algebra u_(k)(3.5)at odd roots.The Poincaré-Birkhoff-Witt(PBW)basis of u_(k)(3.5)is obtained through the basis of q-Schur algebra U(3.5).Then we present a new set for generators and relations for u_(k)(3.5)by PBW basis.
文摘We develop and study the generalization of rational Schur algebras to the super setting.Similar to the classical case,this provides a new method for studying rational supermodules of the general linear supergroup GL(m|n).Furthermore,we establish a Schur-Weyl duality result for rational Schur superalgebras and conclude that under certain conditions these objects will be semisimple.
文摘Let uk （2, r） be a little q-Schur algebra over k, where k is a field containing an ι＇-th primitive root ε of 1 with ι＇〉 4 even, the author constructs a certain monomial base for little q-Schur algebra uk （2, r）.
基金supported by the National Natural Science Foundation of China(Nos.11171325,11371186,11301161)the Research Foundation of Education Bureau of Hubei Province of China(No.Q20131009)
文摘The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ:P → PAP. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations.
文摘This paper is devoted to present some properties of the c-nilpotent multiplier M（c） （L） and some features of c-central extensions of a （finite dimensional） Lie algebra L.Moreover, we give the structure of all c-covers of Lie algebras whose c-nilpotent multipliers have the Hopfian property.
文摘In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKHrpqsllll创串C, defined by: A(ei, ej, ek, es)=ijksa, where the (aijks)s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions rpqsllll哪?(( is not a Banach algebra under schur product.
基金supported by the National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.
基金The first author is supported by Singapore MOE Tier 2 AcRF MOE2015-T2-2-003.
文摘For a partition λ and a prime p,we prove a necessary and sufficient condition for there to exist a composition δ such that δ can be obtained from λ after rearrangement and no partial sums of δ are divisible by p.To demonstrate why we are interested in the question,we compute some signed p-Kostka numbers.
基金the AsiaLink Grant ASI/B7-301/98/679-11the National Natural Foundation of China (Grant No.10501041 and 10301033)
文摘Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then ] induces a full embedding from ￡（△） to eAe-mod which preserves Ext-groups up to certain degrees, where ￡（△） denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq（n,r） with n≥r and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras.
