[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. 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. Then I will speak about the origins of this structure and present what has already been discovered about this new 'type' of algebra (universal algebra, representations, modules, relation to superalgebra,...). After, I am going to give some important examples of Lie antialgebras related to some known structures.
Finally, I am going to present what I am searching for the moment and the questions that I am trying to answer.
Disciplines :
Mathematics
Author, co-author :
Kreusch, Marie ; Université de Liège > Département de mathématique > Géométrie et théorie des algorithmes
Language :
English
Title :
Lie antialgebras
Alternative titles :
[en] Les anti algèbres de Lie
Publication date :
28 June 2011
Event name :
First European Meeting of PhD Students in Mathematics -Amiens
