扭张量积的对偶代数

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-08-01 DOI:10.1007/s10468-025-10353-6

Manuel L. Reyes

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引用次数: 0

摘要

我们研究了两个代数的扭曲张量积的有限对偶协代数是它们各自的有限对偶协代数的共同扭曲张量积的情况。这是通过将有限对偶解释为拓扑对偶来实现的；为了证明这一点，我们证明了连续对偶是开余维有限的线性拓扑向量空间上的强一元函子。我们描述了有限对偶代数上的结果可以应用的一个充分条件，并且我们将这个条件专门用于包括双代数的Ore扩展、粉碎积代数和扭张量积在内的特殊结构。

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Dual Coalgebras of Twisted Tensor Products

We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we specialize this condition to particular constructions including Ore extensions, smash product algebras, and bitwisted tensor products of bialgebras.

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.