The First Hochschild Cohomology as a Lie Algebra

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Datum
2019-04-16MFO Scientific Program
OWLF 2018Serie
Oberwolfach Preprints;2019,09Autor
Rubio y Degrassi, Lleonard
Schroll, Sibylle
Solotar, Andrea
Metadata
Zur LanganzeigeOWP-2019-09
Zusammenfassung
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 solvabilty 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 quantum complete intersections.