Degenerate Sklyanin algebras

• Authors: Andrey Smirnov
• Languages of publication: EN

Abstracts

EN

New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

Keywords

EN

integrable systems; quantum groups; Sklyanin algebras

Discipline

• 02.: Mathematical methods in physics
• 02.20.-a: Group theory(for algebraic methods in quantum mechanics, see 03.65.Fd; for symmetries in elementary particle physics, see 11.30.-j)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2010
• Volume: 8
• Issue: 4
• Pages: 542-554

Dates

published

1 - 8 - 2010

online

22 - 5 - 2010

Contributors

author

Andrey Smirnov

References

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Identifiers

DOI

10.2478/s11534-009-0142-5