The Kauffman bracket skein as an algebra of observables
HTML articles powered by AMS MathViewer
- by Doug Bullock, Charles Frohman and Joanna Kania-Bartoszyńska PDF
- Proc. Amer. Math. Soc. 130 (2002), 2479-2485
Abstract:
We prove that the Kauffman bracket skein algebra of a cylinder over a surface with boundary, defined over complex numbers, is isomorphic to the observables of an appropriate lattice gauge field theory.References
- Doug Bullock, Rings of $\textrm {SL}_2(\textbf {C})$-characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997), no. 4, 521–542. MR 1600138, DOI 10.1007/s000140050032
- Doug Bullock, Charles Frohman, and Joanna Kania-Bartoszyńska, Topological interpretations of lattice gauge field theory, Comm. Math. Phys. 198 (1998), no. 1, 47–81. MR 1657365, DOI 10.1007/s002200050471
- C. Frohman, J. Kania-Bartoszyńska, A matrix model for quantum $SL_2$, preprint, math.QA/0010328.
- Louis H. Kauffman and Sóstenes L. Lins, Temperley-Lieb recoupling theory and invariants of $3$-manifolds, Annals of Mathematics Studies, vol. 134, Princeton University Press, Princeton, NJ, 1994. MR 1280463, DOI 10.1515/9781400882533
- W. B. Raymond Lickorish, An introduction to knot theory, Graduate Texts in Mathematics, vol. 175, Springer-Verlag, New York, 1997. MR 1472978, DOI 10.1007/978-1-4612-0691-0
- Józef H. Przytycki and Adam S. Sikora, On skein algebras and $\textrm {Sl}_2(\textbf {C})$-character varieties, Topology 39 (2000), no. 1, 115–148. MR 1710996, DOI 10.1016/S0040-9383(98)00062-7
- Hans Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987), no. 1, 5–9. MR 873400
Additional Information
- Doug Bullock
- Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
- Email: bullock@math.boisestate.edu
- Charles Frohman
- Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
- MR Author ID: 234056
- ORCID: 0000-0003-0202-5351
- Email: frohman@math.uiowa.edu
- Joanna Kania-Bartoszyńska
- Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
- MR Author ID: 239347
- Email: kania@math.boisestate.edu
- Received by editor(s): November 6, 2000
- Received by editor(s) in revised form: March 16, 2001
- Published electronically: February 12, 2002
- Additional Notes: This research was partially supported by an NSF-DMS Postdoctoral Research Fellowship, and by NSF grants DMS-9803233 and DMS-9971905.
- Communicated by: Ronald A. Fintushel
- © Copyright 2002 by the authors
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2479-2485
- MSC (2000): Primary 57M27, 81T13
- DOI: https://doi.org/10.1090/S0002-9939-02-06323-2
- MathSciNet review: 1897475