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

Linckelmann, M. and 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
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 Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 16 Apr 2020 14:40
URI: https://openaccess.city.ac.uk/id/eprint/24033
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