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
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
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）.
