Linckelmann, M. & Degrassi, L. R. Y. (2020). On the Lie algebra structure of HH1(A) of a finitedimensional algebra A. Proceedings of the American Mathematical Society (PROC), 148(5), pp. 18791890. doi: 10.1090/proc/14875
Abstract
Let A be a split finitedimensional associative unital algebra over a field. The first main result of this note shows that if the Extquiver of A is a simple directed graph, then HH1(A) is a solvable Lie algebra. The second main result shows that if the Extquiver 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 

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