Leibniz Algebras Associated with Representations of Euclidean Lie Algebra
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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In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra n3 and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal Leibniz deformation of n3 with the versal base.
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In this note we present a more detailed and explicit exposition of the definition of a conformal representation of a Leibniz algebra. Recall (arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The idea is based on the general fact that every dialgebra that belongs to a variety Var can be embedded into a conformal algebra of the same variety. In particular, we prove that an ...
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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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This paper studies the relationship between representations of a Lie group and representations of its Lie algebra. We will make the correspondence in two steps: First we shall prove that a given representation of a Lie group will provide us with a corresponding representation of its Lie algebra. Second, we shall go backwards and see whether a given representation of a Lie algebra will have a co...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2019
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-018-09849-1