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

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

2001-12-13

arxiv.org/abs/math/0112141v1

Mathematics

Quantum Algebra

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

Scientific paper

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.

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