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Realization of Lie Algebras of High Dimension via Pseudo-Bosonic Operators
Journal of Lie theory, Tome 30 (2020) no. 4, pp. 925-938
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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.
Classification : 47L60, 17B30, 17B60, 46K10
Mots-clés : Pseudo-bosonic operators, Hilbert space, Schur multiplier, nilpotent Lie algebras, homology 
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     author = {F. Bagarello and F. 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},
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F. Bagarello; F. 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/JLT_2020_30_4_JLT_2020_30_4_a1/