Representation theory of Lie-admissible enveloping algebras on operator algebras: an extension of a theorem by Nelson

Journal Article · Fri Feb 01 04:00:00 EST 1980 · Hadronic J.; (United States)

OSTI ID:6444385

Ghikas, D K.P. ^[1]; Ktorides, C N; Papaloukas, L

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1. Univ. of Patras, Greece

This mathematical note is motivated by an assessment concerning our current understanding of the role of Lie-admissible symmetries in connection with quantum structures. We identify the problem of representations of the universal enveloping (lambda, ..mu..)-mutation algebra of a given Lie algebra on a suitable algebra of operators, as constituting a fundamental first step for improving the situation. We acknowledge a number of difficulties which are peculiar to the adopted nonassociative product for the operator algebra. In view of these difficulties, we are presently content in establishing the generalization, to the Lie-admissible case, of a certain theorem by Nelson. This theorem has been very instrumental in Nelson's treatment concerning the Lie symmetry content of quantum structures. It is hoped that a similar situation will eventually prevail for the Lie-admissible case. We offer a number of relevant suggestions.

• OSTI ID: 6444385
• Journal Information: Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 3:2; ISSN HAJOD
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
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LIE GROUPS
MATHEMATICAL OPERATORS
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SYMMETRY
SYMMETRY GROUPS