The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras in terms of left Banach -modules. It also offers an application of this result to some Lau algebras related to a locally compact group G, such as the Eymard-Fourier algebra A(G), the Fourier-Stieltjes al...

Recently, A.A. Kirillov introduced an interesting class of associative algebras connected with the adjoint representation of G [Ki]. In our paper, such algebras are called g-endomorphism algebras. Each g-endomorphism algebra is a module over the algebra of invariants k[g]; furthermore, it is a direct sum of modules of covariants. Hence it is a free graded finitely generated module over k[g]. Th...

The Method of Model Microfields proposed by Brissaud and Frisch is applied to calculate Stark broadened profiles of hydrogen lines in the static ion approximation. Numerical results for L-a, H-a, and H-ß are found to be in good agreement with those derived from the unified theory by Vidal, Cooper, and Smith over a wide range of plasma densities and temperatures. This demon­ strates that reliabl...

Let g denote a Lie algebra, and let ĝ denote the tensor product of g with a ring of truncated polynomials. The Lie algebra ĝ is called a truncated current Lie algebra. The highest-weight theory of ĝ is investigated, and a reducibility criterion for the Verma modules is described. Let g be a Lie algebra over a field k of characteristic zero, and fix a positive integer N . The Lie algebra (1) ĝ =...

We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C-algebra may be regarded as a result of a quantization procedure. The C-algebra of the tangent groupoid of a given Lie groupoid G (with Lie algebra G) is the C-algebra of a continuous field of C-algebras over R with fibers ...

We extend the definition, from the class of abelian groups to a general locally compact group G, of Feichtinger’s remarkable Segal algebra S0(G). In order to obtain functorial properties for non-abelian groups, in particular a tensor product formula, we endow S0(G) with an operator space structure. With this structure S0(G) is simultaneously an operator Segal algebra of the Fourier algebra A(G)...

Let g be a simple, finite-dimensional Lie (super)algebra, equipped with an embedding of sl2 inducing the minimal gradation on g. The corresponding minimal Walgebra W(g, e−θ) introduced by Kac and Wakimoto has strong generators in weights 1, 2, 3 2 , and all operator product expansions are known explicitly. The weight one subspace generates an affine vertex (super)algebra A(g) where g ⊂ g denote...

Every affine structure on Lie algebra g defines a representation of g in aff(Rn). If g is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra. 200...

We consider the polynomial current Lie algebra gl(n)[x] corresponding to the general linear Lie algebra gl(n), and its factor-algebra gm by the idealPk m gl(n)xk. We construct two families of algebraically independent generators of the center of the universal enveloping algebra U(gm) by using the quantum determinant and the quantum contraction for the Yangian of level m. 0. Introduction Let g b...