Universität zu Köln

Rubio y Degrassi, Lleonard ORCID: 0000-0002-9855-7020, Schroll, Sibylle ORCID: 0000-0001-9618-7647 and Solotar, Andrea . The first Hochschild cohomology as a Lie algebra. Quaest. Math.. ABINGDON: TAYLOR & FRANCIS LTD. ISSN 1727-933X

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Abstract

In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, we show that if the quiver has no parallel arrows and no loops then the first Hochschild cohomology is solvable. For quivers containing loops, we determine easily verifiable sufficient conditions for the solvability of the first Hochschild cohomology. We apply these criteria to show the solvability of the first Hochschild cohomology space for large families of algebras, namely, several families of self-injective tame algebras including all tame blocks of finite groups and some wild algebras including most quantum complete intersections.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Rubio y Degrassi, Lleonard UNSPECIFIED orcid.org/0000-0002-9855-7020 UNSPECIFIED Schroll, Sibylle UNSPECIFIED orcid.org/0000-0001-9618-7647 UNSPECIFIED Solotar, Andrea UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-671719
DOI:	10.2989/16073606.2022.2115424
Journal or Publication Title:	Quaest. Math.
Publisher:	TAYLOR & FRANCIS LTD
Place of Publication:	ABINGDON
ISSN:	1727-933X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language EQUIVALENCE CLASSIFICATION; BLOCKS; HOMOLOGY; FINITE Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67171