Journal article
Unicity for representations of the Kauffman bracket skein algebra
Inventiones mathematicae, Vol.215(2), pp.609-650
02/05/2019
DOI: 10.1007/s00222-018-0833-x
Abstract
This paper resolves the unicity conjecture of Bonahon and Wong for the Kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity. The proof is a consequence of a general unicity theorem that says that the irreducible representations of a prime affine k-algebra over an algebraically closed field k, that is finitely generated as a module over its center, are generically classified by their central characters. The center of the Kauffman bracket skein algebra of any orientable surface at any root of unity is characterized, and it is proved that the skein algebra is finitely generated as a module over its center. It is shown that for any orientable surface the center of the skein algebra at any root of unity is the coordinate ring of an affine algebraic variety.
Details
- Title: Subtitle
- Unicity for representations of the Kauffman bracket skein algebra
- Creators
- Charles Frohman - 0000 0004 1936 8294 grid.214572.7 The University of Iowa Iowa City USAJoanna Kania-Bartoszynska - 0000 0001 1958 7073 grid.431093.c The National Science Foundation Alexandria USAThang Lê - 0000 0001 2097 4943 grid.213917.f Georgia Institute of Technology Atlanta USA
- Resource Type
- Journal article
- Publication Details
- Inventiones mathematicae, Vol.215(2), pp.609-650
- DOI
- 10.1007/s00222-018-0833-x
- ISSN
- 0020-9910
- eISSN
- 1432-1297
- Publisher
- Springer Berlin Heidelberg; Berlin/Heidelberg
- Language
- English
- Date published
- 02/05/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9983985935502771
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