On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras

Cristian Chaparro; Sibylle Schroll; Andrea Solotar

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arXiv · 1811.02211

On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras

Cristian Chaparro·Sibylle Schroll·Andrea Solotar

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Abstract

In this paper we determine the first Hochschild homology and cohomology with different coefficients for gentle algebras and we give a geometrical interpretation of these (co)homologies using the ribbon graph of a gentle algebra as defined in earlier work by the second author. We give an explicit description of the Lie algebra structure of the first Hochschild cohomology of gentle and Brauer graph algebras (with multiplicity one) based on trivial extensions of gentle algebras and we show how the Hochschild cohomology is encoded in the Brauer graph. In particular, we show that except in one low-dimensional case, the resulting Lie algebras are all solvable.

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BibTeX RIS

Cristian Chaparro, Sibylle Schroll, Andrea Solotar. 2020-02-10. On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras. https://arxiv.org/abs/1811.02211

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