A First Sight Towards Primitively Generated Connected Braided Bialgebras

Details A First Sight Towards Primitively Generated Connected Braided Bialgebras A First Sight Towards Primitively Generated Connected Braided Bialgebras

2008-05-22

arxiv.org/abs/0805.3391v3

Mathematics

Quantum Algebra

Scientific paper

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 a sort of universal enveloping algebra of $P$. 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.

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