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arXiv · 2312.14699

The Hochschild cohomology ring of monomial algebras

Dalia Artenstein·Janina C. Letz·Amrei Oswald·Andrea Solotar
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Abstract

We give an explicit description of a diagonal map on the Bardzell resolution for any monomial algebra, and we use this diagonal map to describe the cup product on Hochschild cohomology. Then, we prove that the cup product is zero in positive degrees for triangular monomial algebras. Our proof uses the graded-commutativity of the cup product on Hochschild cohomology and does not rely on explicit computation of the Hochschild cohomology modules.

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BibTeXRIS

Dalia Artenstein, Janina C. Letz, Amrei Oswald, Andrea Solotar. 2023-12-22. The Hochschild cohomology ring of monomial algebras. https://doi.org/10.1016/j.jalgebra.2024.04.019

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