Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894651 | Journal of Geometry and Physics | 2015 | 15 Pages |
Abstract
We study n-ary commutative superalgebras and Lâ-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their n-ary generalizations, commutative associative and Jordan algebras with an invariant form. We give a classification of anti-commutative m-dimensional (mâ3)-ary algebras with an invariant form, and a classification of real simple m-dimensional Lie (mâ3)-algebras with a positive definite invariant form up to isometry. Furthermore, we develop the Hodge Theory for Lâ-algebras with a symmetric invariant form, and we describe quasi-Frobenius structures on skew-symmetric n-ary algebras.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
E.G. Vishnyakova,