A pseudo-Euclidean left-symmetric algebra (A, ., {, }) is a real left-symmetric algebra (A, .) endowed with a non-degenerate symmetric bilinear form { , } such that left multiplication by any element of A is skew-symmetric with respect to { , }. We recall that a pseudo-Euclidean Lie algebra (𝔤, [ , ], { , }) is flat if and only if (𝔤, ., { , }) its underlying vector space endowed with the Levi- Civita product associated with { , } is a pseudo-Euclidean left-symmetric algebra. In this talk, We will give an inductive classification of pseudo-Euclidean left-symmetric algebras (A, ., { , }) such that commutators of all elements of A are contained in the left annihilator of (A, .), these algebras will be called pseudo-Euclidean left-symmetric L−algebras of any signature.
This video is part of the European Non-Associative Algebra Seminar series.
