Frobenius algebras derived from the Kauffman bracket skein algebra

The Kauffman bracket skein algebra of a compact oriented surface when the variable [Formula: see text] in the Kauffman bracket is set equal to [Formula: see text], where [Formula: see text] is an odd counting number, is a central extension of the ring of [Formula: see text]-characters of the fundamental group of the underlying surface. In this paper, we construct symmetric Frobenius algebras from the Kauffman bracket skein algebra of some simple surfaces by two strategies. The first is to localize the skein algebra at the characters so it becomes an algebra over the function field of the character variety of the surface, and the second is to specialize at a place of the character ring.

THE UNIVERSAL CHARACTER RING OF THE (-2, 2m + 1, 2n)-PRETZEL LINK

We explicitly calculate the universal character ring of the (-2, 2m + 1, 2n)-pretzel link and show that it is reduced for all integers m and n.

A Generalized Brauer Induction Theorem and Its Converse

Let G be a finite group, S a unitary subring of the complex number field ℂ and R(G) the character ring of G. Let π be the set of rational prime numbers whose inverses do not belong to S. Denote the family of all p-elementary subgroups of G by W(π), where p runs over π. It is proved that, in the sense of conjugation, W(π) is the least family [Formula: see text] of subgroups of G such that the S-linear map [Formula: see text] is surjective.