728 research outputs found
On -ary Lie algebras of type
These notes are devoted to the multiple generalization of a Lie algebra
introduced by A.M.Vinogradov and M.M.Vinogradov. We compare definitions of such
algebras in the usual and invariant case. Furthermore, we show that there are
no simple -ary Lie algebras of type for
Commutative -ary superalgebras with an invariant skew-symmetric form
We study -ary commutative superalgebras and -algebras that
possess a skew-symmetric invariant form, using the derived bracket formalism.
This class of superalgebras includes for instance Lie algebras and their
-ary generalizations, commutative associative and Jordan algebras with an
invariant form. We give a classification of anti-commutative -dimensional
-ary algebras with an invariant form, and a classification of real
simple -dimensional Lie -algebras with a positive definite invariant
form up to isometry. Furthermore, we develop the Hodge Theory for
-algebras with a symmetric invariant form, and we describe
quasi-Frobenius structures on skew-symmetric -ary algebras.Comment: 27 page
- …