Colloquium du 12-04-2023

Exposé de Alberto Facchini

Le 12-04-2023 à 15:00, en ligne.

Pre-Lie algebras

Résumé

We all have studied groups and rings, and have heard of other algebraic structures like semigroups, Lie algebras, Poisson algebras or Jordan algebras. But other very interesting non-associative or non-distributive algebraic structures have appeared on the scene, helping us to better understand the structure of operations: multiplicative lattices, skew braces, pre-Lie algebras, heaps, trusses,… In this Colloquium we will focus on pre-Lie algebras. Their very first appearance was in the sixties (Gerstenhaber and Vinberg, independently). We will present the first properties of pre-Lie algebras. More generally, we will present the notions of pre-morphism and pre-derivation for arbitrary non-associative algebras over a commutative ring k with identity. These notions will be applied to the study of pre-Lie k-algebras and Lie-admissible k-algebras. Associating with any algebra (A,.) its sub-adjacent anticommutative algebra (A,[-,-]) is a functor from the category of k-algebras with pre-morphisms to the category of anticommutative k-algebras. Pre-morphisms can be dualized in various ways to generalized morphisms (related to pre-Jordan algebras) and anti-pre-morphisms (related to anti-pre-Lie algebras).

Identifiants de connexion

Zoom: ID de réunion : 976 5242 9247 Code secret : 886911