IMAS 23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
artículos
Título:
On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras
Autor/es:
SIBYLLE SCHROLL; CRISTIAN CHAPARRO; ANDREA SOLOTAR
Revista:
JOURNAL OF ALGEBRA
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Lugar: Amsterdam; Año: 2020 vol. 558 p. 293 - 326
ISSN:
0021-8693
Resumen:
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 [32]. 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.
