Grothendieck rings of universal quantum groups

Details Grothendieck rings of universal quantum groups Grothendieck rings of universal quantum groups

2010-06-17

arxiv.org/abs/1006.3464v1

Mathematics

Rings and Algebras

21 pages; submitted for publication

Scientific paper

We determine the Grothendieck ring of finite-dimensional comodules for the free Hopf algebra on a matrix coalgebra, and similarly for the free Hopf algebra with bijective antipode and other related universal quantum groups. The results turn out to be parallel to those for Wang and Van Daele's deformed universal compact quantum groups and Bichon's generalization of those results to universal cosovereign Hopf algebras: in all cases the rings are isomorphic to those of non-commutative polynomials over certain sets, these sets varying from case to case. In most cases we are able to give more precise information about the multiplication table of the Grothendieck ring.

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