Andrei G Bytsko 2008 J. Phys. A: Math. Theor. 41 194003 doi:10.1088/1751-8113/41/19/194003
Baxterization of GLq(2) and its application to the Liouville model and some other models on a lattice
Andrei G Bytsko
Show affiliationsWe develop the Baxterization approach to (an extension of) the quantum group GLq(2). We introduce two matrices which play the role of spectral parameter-dependent L-matrices and observe that they are naturally related to two different comultiplications. Using these comultiplication structures, we find the related fundamental R-operators in terms of powers of coproducts and also give their equivalent forms in terms of quantum dilogarithms. The corresponding quantum local Hamiltonians are given in terms of logarithms of positive operators. An analogous construction is developed for the q-oscillator and Weyl algebras using the fact that their algebraic and coalgebraic structures can be obtained as reductions of those for the quantum group. As an application, the lattice Liouville model, the q-DST model, the Volterra model, a lattice regularization of the free field and the relativistic Toda model are considered.
- PACS
- MSC
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81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
- Subjects
- Dates
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Issue 19 (16 May 2008)
Received 25 January 2008, in final form 19 February 2008
Published 29 April 2008
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Baxterization of GLq(2) and its application to the Liouville model and some other models on a lattice
Andrei G Bytsko 2008 J. Phys. A: Math. Theor. 41 194003
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