The Representation Theory of Brauer Categories I: Triangular Categories

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2022-08-13 DOI:10.1007/s10485-022-09689-7

Steven V Sam, Andrew Snowden

引用次数: 34

Abstract

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple complex Lie algebra, and develop a highest weight theory for them. We show that the Brauer category, the partition category, and a number of related diagram categories admit this structure.

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Brauer范畴的表示理论Ⅰ：三角范畴

这是我们研究Brauer类别及其盟友的表征的系列论文中的第一篇。我们定义了三角范畴的一般概念，抽象了半简单复李代数三角分解的关键性质，并给出了它们的最高权理论。我们证明了Brauer范畴、划分范畴和一些相关的图范畴承认这种结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.