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This Letter is devoted to the building of coherent states from arguments based on classical action–angle variables. First, we show how these classical variables are associated to an algebraic structure in terms of Poisson brackets. In the quantu[...]texto impreso
Using a maximal solvable subalgebra of the Lie algebras gn = sl(2;R)texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía ; Goze, M. | Springer | 2007We present all real solvable algebraically rigid Lie algebras of dimension lower or equal than eight. We point out the differences that distinguish the real and complex classification of solvable rigid Lie algebrastexto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; García Vergnolle, Lucía | Elsevier Science | 2006On montre qu’une algèbre de Lie résoluble rigide réelle n’est pas nécessairement complètement résoluble. On construit un exemple n ? t de dimension minimale dont le tore extérieur t n’est pas formé par des dérivations ad-semi-simples surR. Nous [...]texto impreso
The Beltrametti–Blasi formula that gives the number N(g) of functional independent invariants for the coadjoint representation of a finite dimensional Lie algebra g admits a natural reformulation by means of the Maurer–Cartan equations associate[...]texto impreso
We present a method based on degree one extensions of Lie algebras by a derivation to compute the Casimir operator of perfect Lie algebras having only one invariant for the coadjoint representation and an Abelian radical. In particular, the Casi[...]texto impreso
We show the rigidity of a parameterized family of solvable Leibniz non-Lie algebras in arbitrary dimension, obtaining an irreducible component in the variety L epsilon(n) that does not intersect the variety of Lie algebras non-trivially. Moreove[...]texto impreso
Campoamor Stursberg, Otto Ruttwig | Institute of Mathematics of National Academy of Science of Ukraine | 2006We briefly review a matrix based method to compute the Casimir operators of Lie algebras, mainly certain type of contractions of simple Lie algebras. The versatility of the method is illustrated by constructing matrices whose characteristic poly[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig ; Gonzalez-Gascon, F. | Elsevier | 2003We show that analytic R-3 vector fields having the property of being transversal to either analytic functions or foliations F-2, or parallel. to a foliation, are free from ergodicity and turbulence. The absence of turbulence and ergodicity via i[...]texto impreso
It is shown that for inhomogeneous Lie algebras having only one Casimir operator, the latter can be explicitly constructed from the Maurer-Cartan equations by means of wedge products. It is further proved that this constraint imposes sharp bound[...]texto impreso
A Lie algebra g is called characteristically nilpotent if its algebra of derivations is nilpotent. The authors construct the examples of (2m+2)-dimensional characteristically nilpotent Lie algebras g2m+2 with characteristic sequence c(g2m+2) equ[...]texto impreso
Jacobson’s theorem says that if a finite-dimensiona complex Lie algebra L has a nondegenerate derivation, then L is nilpotent. The converse to this theorem is false. That is, there are nilpotent Lie algebras all of whose derivations are nilpoten[...]texto impreso
A finite-dimensional complex Lie algebra g is characteristically nilpotent if its Lie algebra Derk(g) of derivations is nilpotent. Given two finite-dimensional nilpotent Lie algebras g1, g2, the authors construct a non-split central extension g1[...]texto impreso
Ancochea Bermúdez, José María ; Campoamor Stursberg, Otto Ruttwig | Universidad de Extremadura, Departamento de Matemáticas | 2001Jacobson proved in 1955 that any Lie algebra over a field of characteristic zero which has nondegenerate derivations is nilpotent. Dixmier and Lister proved in 1957 that the converse is false. They provided an example of a new class of Lie algeb[...]
