Homology and central extensions of Leibniz and Lie $n$-algebras
نویسندگان
چکیده
منابع مشابه
Leibniz 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.
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The “coquecigrue” problem for Leibniz algebras is that of finding an appropriate generalization of Lie’s third theorem, that is, of finding a generalization of the notion of group such that Leibniz algebras are the corresponding tangent algebra structures. The difficulty is determining exactly what properties the generalization of group should have. Here we show that Lie racks, smooth left dist...
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The homology of Lie algebras is closely related to the cyclic homology of associative algebras [LQ]. In [L] the first author constructed a "noncommutative" analog of Lie algebra homology which is, similarly, related to Hochschild homology [C, L]. For a Lie algebra g this new theory is the homology of the complex C,(g) ... ~ ~| g|-+ ... ~1 ~ k, whose boundary map d is given by the formula d(gl|1...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2011
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2011.v13.n1.a3