Lie antialgebras

Valentin Ovsienko (1)

1 ICJ - Institut Camille Jordan

We introduce a new class of algebras that we call Lie antialgebras. The subject is situated in between commutative algebra, symplectic/contact geometry and Lie superalgebra theory. We define the odd Lie-Poisson structure on the space dual to a Lie antialgebra and study the notion of central extensions. We classify simple finite-dimensional Lie antialgebras.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Algèbres quantiques [math.QA]; Géométrie symplectique [math.SG]

Valentin Ovsienko. Lie antialgebras. 2007. ⟨hal-00145724v3⟩