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arXiv · 2205.01660

On the Lie algebra structure of integrable derivations

Benjamin Briggs·Lleonard Rubio y Degrassi
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Abstract

Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra $A$ forms a Lie algebra, and a restricted Lie algebra if $A$ contains a field of characteristic $p$. We deduce that the space of integrable classes in $\HH^1(A)$ forms a (restricted) Lie algebra that is invariant under derived equivalences, and under stable equivalences of Morita type between self-injective algebras. We also provide negative answers to questions about integrable derivations posed by Linckelmann and by Farkas, Geiss and Marcos.

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Benjamin Briggs, Lleonard Rubio y Degrassi. 2022-05-03. On the Lie algebra structure of integrable derivations. https://arxiv.org/abs/2205.01660

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