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.
متن کاملLeibniz Algebras, Lie Racks, and Digroups
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...
متن کاملLie $^*$-double derivations on Lie $C^*$-algebras
A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...
متن کاملOn Restricted Leibniz Algebras
In this paper we prove that in prime characteristic there is a functor −p-Leib from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras. Moreover we define the notion of restricted universal enveloping diassociative algebra Udp(g) of a restricted Leibniz algebra g and we show that Ud...
متن کاملJournal of Lie Theory c ○?? Heldermann Verlag Berlin Leibniz algebras, Lie racks, and digroups
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 this generalization should have. Here we show that Lie racks, smooth left distributive...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2013
ISSN: 1815-0659
DOI: 10.3842/sigma.2013.063