Journal article
The structure of the Kauffman bracket skein algebra at roots of unity
Mathematische Zeitschrift, Vol.289(3), pp.889-920
08/2018
DOI: 10.1007/s00209-017-1980-2
Abstract
This paper examines the structure of the Kauffman bracket skein algebra of a punctured surface at roots of unity. A criterion that determines when a collection of skeins forms a basis of the skein algebra as a module over the $$SL(2,{{\mathbb {C}}})$$ SL(2,C) characters of the fundamental group of the surface, with appropriate localization is given. This is used to prove that when the algebra is localized so that every nonzero element of the center has a multiplicative inverse, it is a division algebra. Finally, it is proved that the localized skein algebra can be split as a module over its center as a tensor product of two commutative subalgebras.
Details
- Title: Subtitle
- The structure of the Kauffman bracket skein algebra at roots of unity
- Creators
- Charles Frohman - 0000 0004 1936 8294 grid.214572.7 Department of Mathematics The University of Iowa Iowa City USAJoanna Kania-Bartoszynska - 0000 0001 1958 7073 grid.431093.c Division of Mathematical Sciences The National Science Foundation Alexandria USA
- Resource Type
- Journal article
- Publication Details
- Mathematische Zeitschrift, Vol.289(3), pp.889-920
- DOI
- 10.1007/s00209-017-1980-2
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- Publisher
- Springer Berlin Heidelberg; Berlin/Heidelberg
- Language
- English
- Date published
- 08/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9983985712002771
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