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arXiv · 2506.22924

Comultiplicative map on projective resolution for a family of algebras one of which is cluster-tilted type D4

Pratyush Mishra·Tolulope Oke
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Abstract

We construct a comultiplicative map on the projective bimodule resolution for a family of algebras one of which is cluster-tilted of type D4. The comultiplicative map is presented in terms of idempotents associated with vertices of the quiver and a chain homotopy map is used to describe the multiplicative structure on the Hochschild cohomology ring of the first member of the family. We define a star product used to describe the cup product structure on the Hochschild cohomology ring for all family members.

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Pratyush Mishra, Tolulope Oke. 2025-06-28. Comultiplicative map on projective resolution for a family of algebras one of which is cluster-tilted type D4. https://arxiv.org/abs/2506.22924

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