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Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type

Published online by Cambridge University Press:  24 October 2008

Shahn Majid  and
Martin Markl
Shahn Majid
Affiliation:
Department of Applied Mathematics & Theoretical Physics, University of Cambridge, CB3 9EW. e-mail: majid@damtp.cambridge.ac.uk
Martin Markl
Affiliation:
Mathematical Institute of the Academy, Zitná 25, 115 67 Prague, Czech Republic. e-mail: markl@earn.cvut.cz
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Abstract

We introduce an associative glueing operation ⊕q on the space of solutions of the Quantum Yang–Baxter Equations of Hecke type. The corresponding glueing operations for the associated quantum groups and quantum vector spaces are also found. The former involves 2×2 quantum matrices whose entries are themselves square or rectangular quantum matrices. The corresponding glueing operation for link-invariants is introduced and involves a state-sum model with Boltzmann weights determined by the link invariants to be glued. The standard su(n) solution, its associated quantum matrix group, quantum space and link-invariant arise at once by repeated glueing of the one-dimensional case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 139 - 166
Copyright
Copyright © Cambridge Philosophical Society 1996

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