Universal Enveloping Algebras of Braided Vector Spaces
نویسنده
چکیده
Various attempts to find a proper generalization of the notion of Lie algebra associated to a vector space V endowed with a non symmetric braiding c appeared in the literature. In this direction, we introduce and investigate a notion of braided Lie algebra (and the associated universal enveloping algebra) which turns out to be effective for the class of braided vector spaces (V, c) whose Nichols algebra is obtained dividing out the tensor algebra T (V, c) by the two-sided ideal generated by its primitive elements of degree at least two. One of the main applications of our construction is the description, in terms of universal enveloping algebras, of connected braided bialgebras whose associated graded coalgebra is a quadratic algebra.
منابع مشابه
A First Sight towards Primitively Generated Connected Braided Bialgebras
The main aim of this paper is to investigate the structure of primitively generated connected braided bialgebras A with respect to the braided vector space P consisting of their primitive elements. When the Nichols algebra of P is obtained dividing out the tensor algebra T (P ) by the two-sided ideal generated by its primitive elements of degree at least two, we show that A can be recovered as ...
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