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• W2034008986 startingPage "065205" @default.
• W2034008986 abstract "Given a semidirect product $frak{g}=frak{s}uplusfrak{r}$ of semisimple Lie algebras $frak{s}$ and solvable algebras $frak{r}$, we construct polynomial operators in the enveloping algebra $mathcal{U}(frak{g})$ of $frak{g}$ that commute with $frak{r}$ and transform like the generators of $frak{s}$, up to a functional factor that turns out to be a Casimir operator of $frak{r}$. Such operators are said to generate a virtual copy of $frak{s}$ in $mathcal{U}(frak{g})$, and allow to compute the Casimir operators of $frak{g}$ in closed form, using the classical formulae for the invariants of $frak{s}$. The behavior of virtual copies with respect to contractions of Lie algebras is analyzed. Applications to the class of Hamilton algebras and their inhomogeneous extensions are given." @default.
• W2034008986 created "2016-06-24" @default.
• W2034008986 creator A5044044076 @default.
• W2034008986 creator A5051089439 @default.
• W2034008986 date "2009-01-14" @default.
• W2034008986 modified "2023-10-18" @default.
• W2034008986 title "Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators" @default.
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• W2034008986 doi "https://doi.org/10.1088/1751-8113/42/6/065205" @default.
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