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
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 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.
