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Lie antialgebras: premices

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 نشر من قبل Valentin Ovsienko
 تاريخ النشر 2010
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Valentin Ovsienko




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The main purpose of this work is to develop the basic notions of the Lie theory for commutative algebras. We introduce a class of $mathbbZ_2$-graded commutative but not associative algebras that we call ``Lie antialgebras. These algebras are closely related to Lie (super)algebras and, in some sense, link together commutative and Lie algebras. The main notions we define in this paper are: representations of Lie antialgebras, an analog of the Lie-Poisson bivector (which is not Poisson) and central extensions. We also classify simple finite-dimensional Lie antialgebras.



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