SEMINAR: Groups and Combinatorics Seminar, 16:00 Friday 02/06/2017 in Weatherburn LT: Csaba Schneider
|Groups and Combinatorics Seminar, 16:00 Friday 02/06/2017 in Weatherburn LT: Csaba Schneider
Speaker: Csaba Schneider (Federal University of Minas Gerais, Belo Horizonte)
Title: The isomorphism problem for universal enveloping algebras of Lie algebras
Time and place: 16:00 Friday 02/06/2017 in Weatherburn LT
Abstract: Let U(L) denote the universal enveloping algebra of a Lie algebra L. George Bergman in his influential article of 1978 remarked that it was an open question whether an isomorphism between two universal enveloping algebras U(L) and U(K) implied the isomorphism between the Lie algebras L and K. Since the publication of Bergman’s paper we have learned that the answer to this problem is no. On the other hand, as far as we know, it is a rather rare phenomenon among small-dimensional Lie algebras that non-isomorphic algebras have isomorphic enveloping algebras. This is what makes this problem so interesting.
In the talk, I will review the known results on general Lie algebras and will focus on small-dimensional solvable Lie algebras. I will present some interesting examples to show that isomorphism between universal enveloping algebras is possible without isomorphism of the corresponding Lie algebras.
Future seminars (and past ones back to 2007) may be found at https://www.maths.uwa.edu.au/~glasby/S17.html
Fri, 02 Jun 2017 16:00
Fri, 02 Jun 2017 17:00
Stephen Glasby <[email protected]>
Tue, 30 May 2017 13:13
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