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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hopf algebras of types $U_q(sl_n)'$ and $O_q(SL_n)'$ which give rise to certain invariants of knots, links and 3-manifolds


Authors: Shlomo Gelaki and Sara Westreich
Journal: Trans. Amer. Math. Soc. 352 (2000), 3821-3836
MSC (2000): Primary 16W30
Published electronically: April 18, 2000
MathSciNet review: 1491865
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Abstract:

In this paper we determine when Lusztig's $U_q(sl_n)'$ has all the desired properties necessary to define invariants of knots, links and 3-manifolds. Specifically, we determine when it is ribbon, unimodular and factorizable. We also compute the integrals and distinguished elements involved.


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Additional Information

Shlomo Gelaki
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
Email: shlomi@msri.org

Sara Westreich
Affiliation: Interdisciplinary Department of the Social Science, Bar-Ilan University, Ramat-Gan, Israel
Email: swestric@mail.cc.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02283-2
PII: S 0002-9947(00)02283-2
Received by editor(s): April 2, 1997
Received by editor(s) in revised form: November 12, 1997
Published electronically: April 18, 2000
Additional Notes: This research was supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.
Article copyright: © Copyright 2000 American Mathematical Society