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The Kauffman bracket skein as an algebra of observables

Author(s): Doug Bullock; Charles Frohman; Joanna Kania-Bartoszynska
Journal: Proc. Amer. Math. Soc. 130 (2002), 2479-2485.
MSC (2000): Primary 57M27, 81T13
Posted: February 12, 2002
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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:

1.: D. Bullock, Rings of $SL_2({\mathbb C})$ -characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997), 521-542. MR 98k:57008
2.: D. Bullock, C. Frohman, J. Kania-Bartoszynska, Topological interpretations of Lattice Gauge Field Theory, Comm. Math. Phys. 198 (1998) 47-81. MR 2000b:81107
3.: C. Frohman, J. Kania-Bartoszynska, A matrix model for quantum , preprint, math.QA/0010328.
4.: L. H. Kauffman and S. Lins, Temperley-Lieb recoupling theory and invariants of -manifolds, Ann. of Math. Studies 143, Princeton University Press (1994). MR 95c:57027
5.: W. B. R. Lickorish, An Introduction to Knot Theory, Springer, GTM 175, 1997. MR 98f:57015
6.: J. H. Przytycki, A. S. Sikora, On skein algebras and $SL_2(\mathbb C)$ -character varieties, Topology 39(1) (2000), 115-148. MR 2000g:57026
7.: H. Wenzl, On sequences of projections, C.R. Math. Rep. Acad. Sci. Canada IX, (1987) 5-9. MR 88k:46070

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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
Email: frohman@math.uiowa.edu

Joanna Kania-Bartoszynska
Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
Email: kania@math.boisestate.edu

DOI: 10.1090/S0002-9939-02-06323-2
PII: S 0002-9939(02)06323-2
Received by editor(s): November 6, 2000
Received by editor(s) in revised form: March 16, 2001
Posted: 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 of article: Copyright 2002, by the authors


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