Maurer-Cartan equation for gentle algebras

Published 5 Sep 2023 in math.RA | (2309.02582v1)

Abstract: Let $A= \Bbbk Q/I$ be a finite-dimensional gentle algebra. In this article, under some hypothesis on the quiver $Q$, we give conditions for nilpotency of the $L_\infty$-structure on the shifted Bardzell's complex $B(A)[1]$. For nilpotent cases, we describe Maurer-Cartan elements.

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