| Speaker: Csaba Schneider Affiliation: Federal University of Minas Gerais Time: 14:00 Tuesday, 13 June, 2017 Location: 303-B11 |
| 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. |