Skein algebra of a group

Józef Przytycki; Adam Sikora

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 297-306
  • ISSN: 0137-6934

Abstract

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We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show that skein algebras are isomorphic to the coordinate rings of the corresponding character varieties.

How to cite

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Przytycki, Józef, and Sikora, Adam. "Skein algebra of a group." Banach Center Publications 42.1 (1998): 297-306. <http://eudml.org/doc/208813>.

@article{Przytycki1998,
abstract = {We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show that skein algebras are isomorphic to the coordinate rings of the corresponding character varieties.},
author = {Przytycki, Józef, Sikora, Adam},
journal = {Banach Center Publications},
keywords = {Kauffman bracket skein module},
language = {eng},
number = {1},
pages = {297-306},
title = {Skein algebra of a group},
url = {http://eudml.org/doc/208813},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Przytycki, Józef
AU - Sikora, Adam
TI - Skein algebra of a group
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 297
EP - 306
AB - We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show that skein algebras are isomorphic to the coordinate rings of the corresponding character varieties.
LA - eng
KW - Kauffman bracket skein module
UR - http://eudml.org/doc/208813
ER -

References

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  15. [Pr] J. H. Przytycki, Skein modules of 3-manifolds, Bull. Polish Acad. Science, 39(1-2), 1991, 91-100. 
  16. [P-S-1] J. H. Przytycki, A. S. Sikora, On Skein Algebras And S l 2 ( C ) -Character Varieties, Topology, submitted. Zbl0958.57011
  17. [P-S-2] J. H. Przytycki, A. S. Sikora, in preparation. 
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