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arXiv · 2502.13413

Comparing cohomology via exact split pairs in diagram algebras

Sulakhana Chowdhury·Geetha Thangavelu
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Abstract

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 in [7]. 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.

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Sulakhana Chowdhury, Geetha Thangavelu. 2025-02-19. Comparing cohomology via exact split pairs in diagram algebras. https://arxiv.org/abs/2502.13413

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