Initiation of the representation theory of Lie-admissible algebras of operators on bimodular Hilbert spaces
In this paper we recall the conventional, one-sided, linear theory of modules; we indicate its equivalence with the one-sided representation theory of algebras; and we point out its applicability to associative, Jordan, and Lie algebras. We then outline the broader, two-sided (left and right), linear theory of modules; we indicate its equivalence with the two-sided (left and right), linear theory of modules; we indicate its equivalence with the two-sided representation theory of algebras; and we point out its applicability also to associative, Jordan, and Lie algebras. For the latter algebras, the methods for the implementation of the conventional one-sided representation theory into the broader two-sided theory are also indicated. Furthermore, we show that the alternative algebras generally admit only the two-sided representation theyr for the linear case. These methods are then applied to the initiation of the representation theory of the Lie-asmissible algebras. We first show that these latter algebras, as for the alternative case, generally admit only the two-sided linear representation theory, as a natural generalization of the two-sided theory of the associative and Lie algebras. A number of properties of the two-sided representation theory of the Lie-admissible algebras are pointed tation theory underlying Heisenberg's equations in quantum mechanics is in actuality of two-sided character, although as a trivial implementation of the conventional, one-sided theory. We then recall the Lie-admissible algebras are pointed out.
- Research Organization:
- Harvard Univ., Cambridge, MA
- DOE Contract Number:
- AC02-78ER04742
- OSTI ID:
- 6484260
- Report Number(s):
- CONF-7908175-
- Journal Information:
- Hadronic J.; (United States), Vol. 3:1; Conference: 2. workshop on Lie-admissible formulations, Cambridge, MA, USA, 1 Aug 1979
- Country of Publication:
- United States
- Language:
- English
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658000* - Mathematical Physics- (-1987)