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<p>In this article, we compare the cohomology between the categories of modules of the diagram algebras and the categories of modules of its input algebras. Our main result establishes a sufficient condition for exact split pairs between these two categories, analogous to a work by Diracca and Koenig (J Pure Appl Algebra 212:471–485, 2008). To be precise, we prove the existence of the exact split pairs in <i>A</i>-Brauer algebras, cyclotomic Brauer algebras, and walled Brauer algebras with their respective input algebras.</p>

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Comparing cohomology via exact split pairs in diagram algebras

  • 期刊论文

  • 发表日期：

    2025年6月3日

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  • Sulakhana Chowdhury,
  • Geetha Thangavelu

摘要

In this article, we compare the cohomology between the categories of modules of the diagram algebras and the categories of modules of its input algebras. Our main result establishes a sufficient condition for exact split pairs between these two categories, analogous to a work by Diracca and Koenig (J Pure Appl Algebra 212:471–485, 2008). To be precise, we prove the existence of the exact split pairs in A-Brauer algebras, cyclotomic Brauer algebras, and walled Brauer algebras with their respective input algebras.