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Morita Invariance for Infinitesimal Deformations

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Abstract

Let A and B be two Morita equivalent finite dimensional associative algebras over a field đť•ś. It is well known that Hochschild cohomology is invariant under Morita equivalence. Since infinitesimal deformations are connected with the second Hochschild cohomology group, we explicitly describe the transfer map connecting HH2(A) with HH2(B). This allows us to transfer Morita equivalence between A and B to that between infinitesimal deformations of them. As an application, when đť•ś is algebraically closed, we consider the quotient path algebra associated to A and describe the presentation by quiver and relations of the infinitesimal deformations of A.

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Correspondence to MarĂ­a Julia Redondo.

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Presented by: Pramod Achar

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María Julia Redondo is a research member of CONICET (Argentina). María Julia Redondo and Lucrecia Román have been supported by the project PICT-2015-0366.

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Redondo, M.J., Román, L., Rossi Bertone, F. et al. Morita Invariance for Infinitesimal Deformations. Algebr Represent Theor 25, 1037–1059 (2022). https://doi.org/10.1007/s10468-021-10058-6

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  • DOI: https://doi.org/10.1007/s10468-021-10058-6

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