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SEMINAR: Groups and Combinatorics Seminar, 16:00 Friday 02/06/2017 in Weatherburn LT: Csaba Schneider

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Groups and Combinatorics Seminar, 16:00 Friday 02/06/2017 in Weatherburn LT: Csaba Schneider Other events...
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 Bergmanís 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
Contact Stephen Glasby <[email protected]>
Start Fri, 02 Jun 2017 16:00
End Fri, 02 Jun 2017 17:00
Submitted by Stephen Glasby <[email protected]>
Last Updated Tue, 30 May 2017 13:13
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