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Cohomology of rook-Brauer algebras and their subalgebras
[Submitted on 19 Dec 2024 (v1), last revised 23 Jun 2026 (this v · 2026-06-24 · via math updates on arXiv.org

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Abstract:This paper studies the (co)homology of rook-Brauer algebras and their subalgebras. Our main results focus on the cohomology of rook-Brauer algebras (which is related to the cohomology of symmetric groups), the cohomology of Motzkin algebras (for which we obtain a vanishing result in positive degrees) and the cohomology of walled Brauer algebras (which is related to the cohomology of products of symmetric groups). Along the way we collect some cohomological analogues of known results for Temperley--Lieb algebras, Brauer algebras and rook algebras.

Submission history

From: Andrew Fisher [view email]
[v1] Thu, 19 Dec 2024 14:20:00 UTC (34 KB)
[v2] Tue, 23 Jun 2026 14:18:26 UTC (22 KB)