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  Dynamical systems on quantum tori Lie algebras

Hoppe, J., Olshanetsky, M., & Theisen, S. (1993). Dynamical systems on quantum tori Lie algebras. Communications in Mathematical Physics, 155(3), 429-448. doi:10.1007/BF02096721.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5C33-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5C34-5
Genre: Journal Article

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CommMathPhy155-1993.pdf (Publisher version), 864KB
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 Creators:
Hoppe, Jens1, Author
Olshanetsky, Michail, Author
Theisen, Stefan2, Author              
Affiliations:
1External Organizations, escidoc:persistent13              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 Abstract: We use quantum tori Lie algebras (QTLA), which are a one-parameter family of sub-algebras ofgl infin, to describe local and non-local versions of the Toda systems. It turns out that the central charge of QTLA is responsible for the non-locality. There are two regimes in the local systems-conformal for irrational values of the parameter and non-conformal and integrable for its rational values. We also consider infinite-dimensional analogs of rigid tops. Some of these systems give rise to ldquoquantizedrdquo (magneto-)hydrodynamic equations of an ideal fluid on a torus. We also consider infinite dimensional versions of the integrable Euler and Clebsch cases.

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 Dates: 1993-08
 Publication Status: Published in print
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 Identifiers: eDoc: 379435
DOI: 10.1007/BF02096721
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 155 (3) Sequence Number: - Start / End Page: 429 - 448 Identifier: ISSN: 1432-0916