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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2012, Issue 667


Braided cofree Hopf algebras and quantum multi-brace algebras

Run-Qiang Jian
  • School of Computer Science, Dongguan University of Technology, 1 Daxue Road, Songshan Lake, 523808, Dongguan, P. R. China
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/ Marc Rosso
Published Online: 2011-08-02 | DOI: https://doi.org/10.1515/CRELLE.2011.126


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 B-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.

About the article

Received: 2010-11-08

Revised: 2011-02-14

Published Online: 2011-08-02

Published in Print: 2012-06-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 667, Pages 193–220, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.126.

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