Let Ag=k(x,y)/(x^(2),xy+qyx,y^(2))over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of A_(q)for any q≠O,and the Gerstenhaber algebraic structure o...Let Ag=k(x,y)/(x^(2),xy+qyx,y^(2))over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of A_(q)for any q≠O,and the Gerstenhaber algebraic structure on Hochschild cohomology of A_(q)for q=0.展开更多
In this paper, we prove that there is a natural equivalence between the category F1（x） of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V o...In this paper, we prove that there is a natural equivalence between the category F1（x） of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables.展开更多
We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior alge...We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k.We find a class of comultiplications,such that if√−1∈k,then a quantum complete intersection becomes a bi-Frobe...This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k.We find a class of comultiplications,such that if√−1∈k,then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters qij=±1.Also,it is proved that if√−1∈k then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter q=±√1.While if−1/∈k,then the exterior algebra with two variables admits no bi-Frobenius algebra structures.We prove that the quantum complete intersections admit a bialgebra structure if and only if it admits a Hopf algebra structure,if and only if it is commutative,the characteristic of k is a prime p,and every ai a power of p.This also provides a large class of examples of bi-Frobenius algebras which are not bialgebras(and hence not Hopf algebras).In commutative case,other two comultiplications on complete intersection rings are given,such that they admit non-isomorphic bi-Frobenius algebra structures.展开更多
基金supported by NSFC(Nos.11771122,11801141 and 11961007).
文摘Let Ag=k(x,y)/(x^(2),xy+qyx,y^(2))over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of A_(q)for any q≠O,and the Gerstenhaber algebraic structure on Hochschild cohomology of A_(q)for q=0.
基金supported in part by NSFC #10371036Key Project #2A024 of the Provincial Ministry of Education of Hunan
文摘In this paper, we prove that there is a natural equivalence between the category F1（x） of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables.
基金NSFC#10371036,SRFDP#200505042004 the Cultivation Fund of the Key ScientificTechnical Innovation Project #21000115 of the Ministry of Education of China
文摘We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
基金Supported by National Natural Science Foundation of China(Grant Nos.12131015,11971304)Natural Science Foundation of Shanghai(Grant No.23ZR1435100)。
文摘This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k.We find a class of comultiplications,such that if√−1∈k,then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters qij=±1.Also,it is proved that if√−1∈k then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter q=±√1.While if−1/∈k,then the exterior algebra with two variables admits no bi-Frobenius algebra structures.We prove that the quantum complete intersections admit a bialgebra structure if and only if it admits a Hopf algebra structure,if and only if it is commutative,the characteristic of k is a prime p,and every ai a power of p.This also provides a large class of examples of bi-Frobenius algebras which are not bialgebras(and hence not Hopf algebras).In commutative case,other two comultiplications on complete intersection rings are given,such that they admit non-isomorphic bi-Frobenius algebra structures.
