Journal article
The Localized Skein Algebra is Frobenius
Algebraic & geometric topology, Vol.17(6), pp.3341-3373
01/12/2015
DOI: 10.2140/agt.2017.17.3341
Abstract
Algebr. Geom. Topol. 17 (2017) 3341-3373 When $A$ in the Kauffman bracket skein relation is a primitive $2N$th root of unity, where $N\geq 3$ is odd, the Kauffman bracket skein algebra $K_N(F)$ of a finite type surface $F$ is a ring extension of the $SL_2\mathbb{C}$-characters $\chi(F)$ of the fundamental group of $F$. We localize by inverting the nonzero characters to get an algebra $S^{-1}K_N(F)$ over the function field of the character variety. We prove that if $F$ is noncompact, the algebra $S^{-1}K_N(F)$ is a symmetric Frobenius algebra. Along the way we prove $K(F)$ is finitely generated, $K_N(F)$ is a finite rank module over $\chi(F)$, and the simple closed curves that make up any simple diagram on $F$ generate a finite field extension of $S^{-1}\chi(F)$ inside $S^{-1}K_N(F)$.
Details
- Title: Subtitle
- The Localized Skein Algebra is Frobenius
- Creators
- Nel AbdielCharles Frohman
- Resource Type
- Journal article
- Publication Details
- Algebraic & geometric topology, Vol.17(6), pp.3341-3373
- DOI
- 10.2140/agt.2017.17.3341
- ISSN
- 1472-2747
- eISSN
- 1472-2739
- Language
- English
- Date published
- 01/12/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985958902771
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