Lax equations on Lie superalgebras
Автор: Karabanov A.
Журнал: Известия Коми научного центра УрО РАН @izvestia-komisc
Рубрика: Научные статьи
Статья в выпуске: 5 (71), 2024 года.
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It is demonstrated that the standard construction of Lax equations on Lie algebras can be extended to Lie superalgebras, with the even subspace carrying the usual Lax equations. The extended equations inherit the existence of the canonical trace polynomial integrals of motion. An extra set of integrals exists in the odd subspace, with a nontrivial homological structure of the orbit space. This establishes a curious algebraic link between integrable evolution equations, supersymmetry and the deformation theory.
Lie superalgebras, lax equations, integrals of motion, homological algebra, deformation theory
Короткий адрес: https://sciup.org/149146265
IDR: 149146265 | DOI: 10.19110/1994-5655-2024-5-5-10
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