标题： 关于阿贝尔张量范畴中的Rosenberg-Zelinsky序列 显示英文标题

标题： On the Rosenberg-Zelinsky sequence in abelian monoidal categories

摘要： 我们考虑某些阿贝尔张量范畴中的弗罗贝尼乌斯代数及其双模。 特别是我们研究弗罗贝尼乌斯代数上双模范畴的Picard群，即可逆双模的同构类的群。 Rosenberg-Zelinsky序列描述了一个从代数自同构群到Picard群的同态，但通常不是满射的。 我们研究在什么条件下存在一个Morita等价的弗罗贝尼乌斯代数，使得相应的同态是满射的。 我们考虑的一个动机是共形场论中的轨道构造。 显示英文摘要

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.