Braided cofree Hopf algebras and quantum multi-brace algebras

Details Braided cofree Hopf algebras and quantum multi-brace algebras Braided cofree Hopf algebras and quantum multi-brace algebras

2009-04-20

arxiv.org/abs/0904.2964v4

Mathematics

Quantum Algebra

26 pages, Latex; the title is changed; some statements are improved; accepted for the publication in Crelle's Journal

Scientific paper

We give a systematic construction of Hopf algebra structures on braided cofree coalgebras. The relevant underlying structures are braided algebras and braided coalgebras. We provide some interesting examples of these algebras and coalgebras related to quantum groups. We introduce quantum multi-brace algebras which are generalizations of both braided algebras and $\textbf{B}_\infty$-algebras, as the natural framework. This new subject enables one to quantize some important algebra structures in a uniform way. Particular interesting examples are quantum quasi-shuffle algebras.

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