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Drinfeld-Sokolov hierarchies on truncated current Lie algebras. (English) Zbl 1248.37063
Crespo, Teresa (ed.) et al., Algebraic methods in dynamical systems. Proceedings of the conference, Będlewo, Poland, May 16–22, 2010. Dedicated to Michael Singer on his 60th birthday. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-13-3/pbk). Banach Center Publications 94, 163-171 (2011).
The aim of this paper is to generalize the Drinfeld-Sokolov construction of integrable hierarchies. Recall that the Drinfeld-Sokolov construction provides an integrable hierarchy by an affine Kac-Moody Lie algebra and a vertex of its Dynkin diagram. The paper generalizes this construction to so-called truncated current Lie algebras (certain quotients of current Lie algebras). After a brief description of truncated current Lie algebras and their properties, a construction of integrable equations by means of Lax representation is given.
For the entire collection see [Zbl 1230.00043].
MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B69 Vertex operators; vertex operator algebras and related structures
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
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