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Quantum dissipative systems: IV. Analogues of Lie algebras and groupsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
- Автор: Tarasov V.E.
- Журнал: Theoretical and Mathematical Physics
- Том: 110
- Номер: 2
- Год издания: 1997
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 168
- Последняя страница: 178
- DOI: 10.1007/BF02630442
- Аннотация: The condition of self-consistency for the quantum description of dissipative systems makes it necessary to exceed the limits of Lie algebras and groups, i.e., this requires the application of non-Lie algebras (in which the Jacobi identity does not hold) and analytic quasi-groups (which are nonassociative generalizations of groups). In the present paper, we show that the analogues of Lie algebras and groups for quantum dissipative systems are utants are Lie subalgebras) and analytic commutant-associative loops (whose commutants are associative subloops (groups)). It is proved that the tangent algebra of an analytic commutant-associative loop with invertibility (a Valya loop) is a commutant-Lie algebra (a Valya algebra). Some examples of commutant-Lie algebras are considered.
- Добавил в систему: Тарасов Василий Евгеньевич