具有若干对象的余代数上的纠缠模和控制模：Frobenius定理、可分性定理和Maschke定理

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-07-07 DOI:10.1016/j.jalgebra.2025.07.001

Abhishek Banerjee , Surjeet Kour

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引用次数: 0

摘要

利用具有多个对象的余代数的作用，研究了范畴商上的类模对象。它们以三组（C, a, ψ）上的“缠绕小模”和“缠绕控制模”的形式存在，其中a是一个代数，C是一个有几个对象的协代数，ψ是将C与a“缠绕”在一起的映射集合。我们的目标是证明缠绕小模和缠绕控制模之间的函子的Frobenius定理、可分性定理和Maschke型定理。

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Entwined comodules and contramodules over coalgebras with several objects: Frobenius, separability and Maschke theorems

We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of “entwined comodules” and “entwined contramodules” over a triple

(C, A, ψ)

, where A is an algebra,

C

is a coalgebra with several objects and ψ is a collection of maps that “entwines”

C

with A. Our objective is to prove Frobenius, separability and Maschke type theorems for functors between categories of entwined comodules and entwined contramodules.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.