On the structure of a Lie-admissible algebra in the space of Gâteaux differentiable operators
type: Item
instance of: scholarly article
title: On the structure of a Lie-admissible algebra in the space of Gâteaux differentiable operators
zbMATH Open document ID: 0834.46032
DOI: 10.1007/BF02110774
author: Vladimir M. Savchin
published in: Mathematical Notes
publication date: 1995-09-24T00:00:00Z
review text: By an algebra we shall mean a linear, in general, nonassociative algebra over the field \(\mathbb{R}\) of real numbers. An algebra \(\langle A,(*)\rangle\) is said to be Lie-admissible if the linear space \(A\), endowed by the bilinear operation \[ [a, b]= a* b- b* a\qquad \forall a, b\in A \] is a Lie algebra. Structures of the mentioned form have applications in classical mechanics and in theoretical physics. In connection with this it is of interest to describe various Lie-admissible operations \((*)\) in given linear spaces. The purpose of this note is to describe a very general structure of a Lie-admissible algebra in the real linear space of Gâteaux differentiable operators.
Mathematics Subject Classification ID: 46H70
Mathematics Subject Classification ID: 17D25
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 796775
zbMATH Keywords: Lie-admissible operations
zbMATH Keywords: Lie-admissible algebra
zbMATH Keywords: real linear space of Gâteaux differentiable operators
MaRDI profile type: Publication
Wikidata QID: Q115392744
cites work: Q3321501
cites work: Q5645931
cites work: An operator approach to Poisson brackets
full work available at URL: https://doi.org/10.1007/bf02110774
OpenAlex ID: W1967429525
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description: scientific article; zbMATH DE number 796775