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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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Kronecker's Method and Complete Systems of Functions in Bi-Involution on Classical Lie Algebrasстатья
- Автор: Garazha Aleksandra
- Журнал: Journal of Lie Theory
- Том: 33
- Номер: 2
- Год издания: 2023
- Издательство: Heldermann Verlag
- Местоположение издательства: Germany
- Первая страница: 663
- Последняя страница: 686
- Аннотация: We use Kronecker's method to construct systems of functions in bi-involution with respect to two Poisson brackets: the canonical one and the bracket with frozen argument A \in g. For the Lie algebras sl_n and sp_2n, we construct complete systems of functions in bi-involution for any A \in g. For the Lie algebras so_2n+1 and so_2n, we describe elements A such that we can construct a complete system of functions in bi-involution and the elements A such that we can construct the Kronecker part of a complete system of functions in bi-involution. Also, we prove that the constructed functions freely generate some limits of Mishchenko-Fomenko subalgebras. Finally, for the Lie algebras sl_n and sp_2n, we show that the Kronecker indices are the same for all elements A in any given sheet, while for the Lie algebras so_2n and so_2n+1, we give examples of sheets such that this is not true.
- Добавил в систему: Гаража Александра Андреевна