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On the classification of automorphic Lie algebras. (English) Zbl 1239.17025

Automorphic Lie algebras are useful in studying reductions of integrable systems and also interesting in their own right. It is a class of infinite dimensional algebras generalizing graded Lie algebras. In the present article the complete classification of automorphic Lie algebras associated with the \(\text{sl}(2,\mathbb C)\) case is given.

MSC:

17B65 Infinite-dimensional Lie (super)algebras
17B80 Applications of Lie algebras and superalgebras to integrable systems
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures

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