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This article is cited in 1 scientific paper (total in 1 paper)
Lax operators, Poisson groups, and the differential Galois theory
M. A. Semenov-Tian-Shanskyab a St. Petersburg Branch of the Steklov Institute of Mathematics , RAS, St. Petersburg, Russia
b Institut de Mathématiques de Bourgogne, Dijon, France
Abstract:
We examine the transfer of a Poisson structure in a space of differential or difference Lax operators to the space of solutions of the corresponding auxiliary problem (the space of wave functions) in detail. We investigate a spontaneous symmetry breaking resulting in the appearance of a nontrivial Poisson structure on the differential or difference Galois group. We review the difference version of the Drinfeld–Sokolov theory and describe a new type of classical $r$-matrices related to generalized exchange algebras.
Keywords:
Poisson reduction, Poisson–Lie group, classical $r$-matrix, difference operator, differential Galois group, difference Galois group.
Received: 11.06.2014
Citation:
M. A. Semenov-Tian-Shansky, “Lax operators, Poisson groups, and the differential Galois theory”, TMF, 181:1 (2014), 173–199; Theoret. and Math. Phys., 181:1 (2014), 1279–1301
Linking options:
https://www.mathnet.ru/eng/tmf8729https://doi.org/10.4213/tmf8729 https://www.mathnet.ru/eng/tmf/v181/i1/p173
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Abstract page: | 534 | Full-text PDF : | 225 | References: | 65 | First page: | 40 |
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