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arXiv · 1708.02933

On geometric degenerations and Gerstenhaber formal deformations

Sergio Chouhy
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Abstract

We study the degeneration relations on the varieties of associative and Lie algebra structures on a fixed finite dimensional vector space and give a description of them in terms of Gerstenhaber formal deformations. We use this result to show how the orbit closure of the $3$-dimensional Lie algebras can be determined using homological algebra. For the case of finite dimensional associative algebras, we prove that the $N$-Koszul property is preserved under the degeneration relation for all $N\geq2$.

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Sergio Chouhy. 2017-08-09. On geometric degenerations and Gerstenhaber formal deformations. https://doi.org/10.1112/blms.12277

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