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arXiv · 2411.04614

Crossed modules and cohomology of algebras over an operad

Johan Leray·Salim Rivière·Friedrich Wagemann
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Abstract

We introduce a general definition of a $n$-crossed module of $P$-algebras over an algebraic operad $P$, which coincides with historical definitions in the cases of the operads As and Lie and $n = 1$. We establish a natural isomorphism between the abelian group of equivalence classes of $n$-crossed modules over a pair $(A,M)$ for an operad $P$ and the $(n+1)^\text{th}$ operadic cohomology group of $A$ with coefficients in $M$.

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Johan Leray, Salim Rivière, Friedrich Wagemann. 2024-11-07. Crossed modules and cohomology of algebras over an operad. https://doi.org/10.2140/agt.2026.26.2635

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