Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras

2001/12/13 by Cyrille Ospel, Ospel, Cyrille
Mathematics · #16W30 (Primary) 17B37 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0112141

23 pages, 7 Postscript figures (uses epsfig.sty)

arxiv created 2001/12/13 · arxiv updated 2009/11/30

Abstract

For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first application we show that the Hochschild-Serre identity is the dual statement of our result. In particular, we extend this identity to Hopf algebras. Secondly, we clarify the construction of a class of quasi-Hopf algebras.

Related

• Quasi-shuffle products
• Explicit results concerning quantum quasi-shuffle algebras and their applications
• A Borel-Weil-Bott type theorem of quantum shuffle algebras
• Cross Product Quantisation, Nonabelian Cohomology And Twisting Of Hopf Algebras
• Hopf Semialgebras