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
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