منابع مشابه
Forum Mathematicum Leibniz N-algebras
A Leibniz n-algebra is a vector space equipped with an n-ary operation which has the property of being a derivation for itself. This property is crucial in Nambu mechanics. For n 2 this is the notion of Leibniz algebra. In this paper we prove that the free Leibniz n 1algebra can be described in terms of the n-magma, that is the set of n-ary planar trees. Then it is shown that the n-tensor ...
متن کاملCARTAN SUBALGEBRAS OF LEIBNIZ n-ALGEBRAS
The present paper is devoted to the investigation of properties of Cartan subalgebras and regular elements in Leibniz n-algebras. The relationship between Cartan subalgebras and regular elements of given Leibniz n-algebra and Cartan subalgebras and regular elements of the corresponding factor n-Lie algebra is established. 1 Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-...
متن کاملLeibniz Algebras and Lie Algebras
This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
متن کاملCup-product for Leibniz Cohomology and Dual Leibniz Algebras
For any Lie algebra g there is a notion of Leibniz cohomology HL(g), which is defined like the classical Lie cohomology, but with the n-th tensor product g⊗n in place of the n-th exterior product Λ g. This Leibniz cohomology is defined on a larger class of algebras : the Leibniz algebras (cf. [L1], [L2]). A Leibniz algebra is a vector space equipped with a product satisfying a variation of the ...
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ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2016
ISSN: 1005-3867,0219-1733
DOI: 10.1142/s1005386716000249