Crossed Homomorphisms on associative superalgebras

RB Yadav; Arpan Sharma

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arXiv · 2608.06436

Crossed Homomorphisms on associative superalgebras

RB Yadav·Arpan Sharma

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Abstract

In this paper, we introduce the notion of crossed homomorphisms on associative superalgebras. We show that crossed homomorphisms are precisely the Maurer--Cartan elements of a naturally associated graded Lie algebra. This characterization enables us to construct a cohomology theory of crossed homomorphisms. We then investigate formal deformations of crossed homomorphisms and derive the corresponding deformation equations. It is proved that the infinitesimal part of a formal deformation is a 1-cocycle in the associated cohomology, while the obstruction to extending a deformation of finite order is a 2-cocycle.

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RB Yadav, Arpan Sharma. 2026-08-06. Crossed Homomorphisms on associative superalgebras. https://arxiv.org/abs/2608.06436

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