Title: Representation theory of Lie-admissible enveloping algebras on operator algebras: an extension of a theorem by Nelson
Abstract: 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.
Publication Year: 1980
Publication Date: 1980-02-01
Language: en
Type: article
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