Vinberg left-symmetric algebras

25/01/2019, 14:00 - 15:00 in MAP/0G/018

Cartier, Pierre (IHES Paris)


Abstract:

Starting from problems in differential geometry, Vinberg introduced a new class of algebras, with a left-symmetric associator. A similar class was introduced by Gerstenhaber under the name of pre-Lie algebra. There are many situations where a Lie algebra is derived from a pre-Lie algebra via antisymmetrisation, and this fits well under Loday’s magic square. We shall review the basic facts of this class of algebras, together with some of the applications in geometry, algebra and combinatorics.