1Dip. di Ingegneria, Università di Palermo, 90128 Palermo, Italy 2Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, 80126 Napoli, Italy 3Dept. of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa
Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 925-938
The present paper is the third contribution of a series of works, where we investigate pseudo-bosonic operators and their connections with finite dimensional Lie algebras. We show that all finite dimensional nilpotent Lie algebras (over the complex field) can be realized by central extensions of Lie algebras of pseudo-bosonic operators. This result is interesting, because it provides new examples of dynamical systems for nilpotent Lie algebras of any dimension. One could ask whether these operators are intrinsic with the notion of nilpotence or not, but this is false. In fact we exibit both a simple Lie algebra and a solvable nonnilpotent Lie algebra, which can be realized in terms of pseudo-bosonic operators.
1
Dip. di Ingegneria, Università di Palermo, 90128 Palermo, Italy
2
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, 80126 Napoli, Italy
3
Dept. of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa
Fabio Bagarello; Francesco G. Russo. Realization of Lie Algebras of High Dimension via Pseudo-Bosonic Operators. Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 925-938. http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a1/
@article{JOLT_2020_30_4_a1,
author = {Fabio Bagarello and Francesco G. Russo},
title = {Realization of {Lie} {Algebras} of {High} {Dimension} via {Pseudo-Bosonic} {Operators}},
journal = {Journal of Lie Theory},
pages = {925--938},
year = {2020},
volume = {30},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a1/}
}
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AU - Fabio Bagarello
AU - Francesco G. Russo
TI - Realization of Lie Algebras of High Dimension via Pseudo-Bosonic Operators
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