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Abstract :
[en] Lie antialgebras which is a $\Z_2$-graded commutative algebra (but not associative) was introduced in 2007 by Valentin Ovsienko. This notion takes place in the superspaces theory studied since years in geometry. This algebra was discovered in the context of symplectic geometry. In a way, Lie antialgebras unify in a special meaning associative and commutative algebras with Lie algebras. Since this is quite a new subject a lot of things have to be done in the understanding of this structure.
At first, I am going to explain the notion of superspaces and in particular the one of Lie superalgebras and give some important examples. After I am going to introduce the topic of Lie antialgebras and also give some examples. And finally I am going to give a links between them (Lie antilagebra and Lie superalgebra).
If I have time, I will probably speak a bit about extensions and relations with 2-cocycles in the cohomology theory. That's what I am interested in for the moment.
