## On the Lie algebra structure of HH1(A) of a finite-dimensional algebra A

Linckelmann, M. & Degrassi, L. R. Y. (2020).
On the Lie algebra structure of HH1(A) of a finite-dimensional algebra A.
*Proceedings of the American Mathematical Society (PROC)*, 148(5),
pp. 1879-1890.
doi: 10.1090/proc/14875

## Abstract

Let A be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of A is a simple directed graph, then HH1(A) is a solvable Lie algebra. The second main result shows that if the Ext-quiver of A has no loops and at most two parallel arrows in any direction, and if HH1(A) is a simple Lie algebra, then char(k)neq2 and HH1(A)2(k). The third result investigates symmetric algebras with a quiver which has a vertex with a single loop.

Publication Type: | Article |
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Additional Information: | First published in Proceedings of the American Mathematical Society in 148 (2020), published by the American Mathematical Society. © Copyright 2020 American Mathematical Society. |

Subjects: | Q Science > QA Mathematics |

Departments: | School of Science & Technology > Mathematics |

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Available under License Creative Commons Attribution Non-commercial No Derivatives.

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