Little q-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups by Du, Fu and Wang. In this paper, we obtain a presentation by generators and relations for little q-Schur algebras uk...Little q-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups by Du, Fu and Wang. In this paper, we obtain a presentation by generators and relations for little q-Schur algebras uk（2, r）.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
introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality relate...introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.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
文摘Little q-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups by Du, Fu and Wang. In this paper, we obtain a presentation by generators and relations for little q-Schur algebras uk（2, r）.
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.
基金supported by the National Natural Science Foundation of China(NSFC)Grant 12071136.
文摘introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.
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.
