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SUMMARY:Saïd Benayadi (University of Lorraine\, France)
DTSTART:20240212T150000Z
DTEND:20240212T160000Z
DTSTAMP:20260423T035617Z
UID:ENAAS/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/56/">O
 n a class of pseudo-Euclidean left-symmetric algebras</a>\nby Saïd Benaya
 di (University of Lorraine\, France) as part of European Non-Associative A
 lgebra Seminar\n\n\nAbstract\nA pseudo-Euclidean left-symmetric algebra $(
 A\, .\,< \, >)$ is a real left-symmetric algebra $(A\,.)$ endowed with a n
 on-degenerate symmetric bilinear  form $< \, >$ such that left multiplicat
 ions by any element of A are skew-symmetric with respect to $< \, >$. We r
 ecall that a pseudo-Euclidean Lie algebra $(g\, [ \, ]\, < \, >)$ is flat 
 if and only if $(g\, .\, \,< \, >)$  its underlying vector space endowed w
 ith the Levi-Civita product associated with $< \, >$ is a pseudo-Euclidean
  left-symmetric algebra. In this talk\, We will give an inductive classifi
 cation of  pseudo-Euclidean left-symmetric algebras $(A\, .\,< \, >)$ such
  that commutators of allelements of A are contained in the left annihilato
 r of $(A\, .)\,$ these algebras will be called pseudo-Euclidean left-symme
 tric L−algebras of any signature. To do this\, we will develop double ex
 tension processes that allow us to have inductive descriptions of all pseu
 do-Euclidean left-symmetric $L$−algebras and of all its pseudo-Euclidean
  modules.\n
LOCATION:https://researchseminars.org/talk/ENAAS/56/
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