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arXiv · 2505.21977

Homology of Rook-Brauer Algebras and Motzkin Algebras

Khoa Ta
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Abstract

Using the technique of inductive resolution introduced in arXiv:2303.07979, we prove that the homology of Rook-Brauer Algebra, interpreted as appropriate Tor-group, is isomorphic to that of symmetric group for all degrees under the assumption that $\epsilon$ in $R$ is invertible; furthermore, we also prove the homology of the Motzkin algebras vanishes in positive degrees under the same assumption. These results thereby establish homological stability of both algebras.

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Khoa Ta. 2025-05-28. Homology of Rook-Brauer Algebras and Motzkin Algebras. https://arxiv.org/abs/2505.21977

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