A class of Lie racks associated to symmetric Leibniz algebras
نویسندگان
چکیده
We classify symmetric Leibniz algebras in dimensions 3 and 4 we determine all associated Lie racks. Some of such racks give rise to nontrivial topological quandles. study some algebraic properties these quandles a necessary sufficient condition for them be quasi-trivial.
منابع مشابه
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 the generalization of group should have. Here we show that Lie racks, smooth left dist...
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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 this generalization should have. Here we show that Lie racks, smooth left distributive...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2021
ISSN: ['1793-6829', '0219-4988']
DOI: https://doi.org/10.1142/s0219498822502309