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Lie algebras generated by dynamical systems. (English. Russian original) Zbl 0848.17036

St. Petersbg. Math. J. 4, No. 6, 1143-1151 (1993); translation from Algebra Anal. 4, No. 6, 103-113 (1992).
Summary: The author defines the class of infinite-dimensional \(\mathbb{Z}\)-graded Lie algebras generated by dynamical systems and shows that these algebras are a special case of Lie algebras with continuous root system, defined in M. V. Savel’ev and the author, Commun. Math. Phys. 126, 367-378 (1989; Zbl 0691.17012) and New examples of continuum graded Lie algebras, Phys. Lett. A 143, 121-128 (1990)]. He establishes a precise isomorphism between “sine-algebras” and “rotation-Lie-algebras”, and gives other examples. He briefly mentions algebras of the type \((B)\), \((D)\), and \((C)\) for a dynamical system.

MSC:

17B70 Graded Lie (super)algebras
17B65 Infinite-dimensional Lie (super)algebras
22E70 Applications of Lie groups to the sciences; explicit representations
46L55 Noncommutative dynamical systems

Citations:

Zbl 0691.17012
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