论文标题
量子完整交叉点上的Bi-Frobenius代数结构
Bi-Frobenius algebra structure on quantum complete intersections
论文作者
论文摘要
本文是在量子完整交叉点上寻找Bi-Frobenius代数结构。我们找到一类的合作，以便如果$ \ sqrt {-1} \在k $中，那么量子完整的交集将变成bi-frobenius algebra，并且仅当所有参数$ q_ {ij} = ij} = \ pm pm 1 $时，且仅当所有参数$ q_ Q_ {ij} = \ pm pm 1 $。另外，可以证明，如果$ \ sqrt {-1} \在k $中，则两个变量中的量子外部代数在且仅当参数$ q = \ pm 1 $时，就会允许Bi-Frobenius代数结构。虽然如果$ \ sqrt {-1} \ notin k $，则具有两个变量的外部代数不承认Bi-Frobenius代数结构。由于特征零字段上的量子完全交点不承认任何双重结构，因此这给出了一类Bi-frobenius代数的示例，这些代数不是双齿的（因此不hopf代数）。另一方面，量子外部代数在且仅当$ {\ rm char} \ k = 2 $时接受了bialgebra结构。在交换性的情况下，给出了其他两项在完全交叉环环上的合并，以便它们接纳非晶状体二型纤维纤维代数代数结构。
This paper is to look for bi-Frobenius algebra structures on quantum complete intersections. We find a class of comultiplications, such that if $\sqrt{-1}\in k$, then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters $q_{ij} = \pm 1$. Also, it is proved that if $\sqrt{-1}\in k$ then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter $q = \pm 1$. While if $\sqrt{-1}\notin k$, then the exterior algebra with two variables admits no bi-Frobenius algebra structures. Since a quantum complete intersection over a field of characteristic zero admits no bialgebra structures, this gives a class of examples of bi-Frobenius algebras which are not bialgebras (and hence not Hopf algebras). On the other hand, a quantum exterior algebra admits a bialgebra structure if and only if ${\rm char} \ k = 2$. In commutative case, other two comultiplications on complete intersection rings are given, such that they admit non-isomorphic bi-Frobenius algebra structures.
