Generalized Serre relations for Lie algebras associated with positive unit forms

Gromov introduced translation algebras (over the real or complex fields) in the early 1990’s as certain algebras of infinite matrices, whose entries are indexed by a given

While the preceding papers mostly considered abstract properties of algebras of quotients, our main objective is to compute Q m (L) for some Lie algebras L. Specifically, we

Our review covers: the Darboux-Lie theorem which gives the local structure of the foliation, and the affine structure of the leaves, Weinstein's theorem of tubular equivalence with

One can consider a Jacobi manifold as a generalized phase-space and the Lie algebra of infinitesimal automorphisms as the algebra of symmetries of this phase-space.. Then the

We have seen that modifications of the procedure to compute the Casimir operators of semidirect products s − → ⊕ R w(n) using quadratic operators in the enveloping algebra can

This non- trivial response of the phase under gauge transformations causes a deformation of the corresponding Lie-algebra commutators and leads to the appearance of central

These algebras naturally appear as a residual gauge symmetry in the theory of relativistic membranes [3], which exhibits an intriguing connection with the quantum mechanics of

Keywords: Infinite-dimensional Lie algebras, Virasoro and W ∞ symmetries, Berezin and geo- metric quantization, coherent states, operator symbols, classical limit, Poisson