交换幺半范畴中的Rosenberg-Zelinsky序列
On the Rosenberg-Zelinsky sequence in abelian monoidal categories
摘要：
研究了交换幺半范畴范畴中的Frobenius代数及其双模.特别地，我们研究了Frobenius代数上双模范畴的Picard群，即可逆双模的同构类群。罗森伯格-泽林斯基序列描述了从代数自同构群到皮卡德群的同态，但它通常不是满射的。研究了在什么条件下存在一个Morita等价的Frobenius代数，其对应的同态是满射的。我们考虑的一个动机是共形域论中的轨道结构。
英文摘要：
We consider Frobenius algebras and their bimodules in certain abelian monoidal categories. In particular we study the Picard group of the category of bimodules over a Frobenius algebra, i.e. the group of isomorphism classes of invertible bimodules. The Rosenberg-Zelinsky sequence describes a homomorphism from the group of algebra automorphisms to the Picard group, which however is typically not surjective. We investigate under which conditions there exists a Morita equivalent Frobenius algebra for which the corresponding homomorphism is surjective. One motivation for our considerations is the orbifold construction in conformal field theory.
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