CONSTRUCTION OF A COMPACT QUANTUM GROUP FOR
TRANSPOSITION-COLORING FUNCTION
Abstract: We apply the Woronowicz construction of compact quantum group to the function
which associates different parameters (colors) with transpositions generating the set of
four-element permutation. We show that in the case when one of the parameters equals one,
we get a non-trivial (non-commutative) compact quantum group which is a twisted product of
and the two-dimensional torus.
2000 AMS Mathematics Subject Classification: Primary: 81R50; Secondary:
20G42.
Keywords and phrases: Quantum groups, twisted determinant condition, twisted
product.