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On the CR-structure of certain linear group orbits in infinite dimensions

Wilhelm Kaup (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

For large classes of complex Banach spaces (mainly operator spaces) we consider orbits of finite rank elements under the group of linear isometries. These are (in general) real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits  M explicitly and show as main result that every continuous CR-function on  M has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite...

On the definition of the dual Lie coalgebra of a Lie algebra.

Bertin Diarra (1995)

Publicacions Matemàtiques

Let L be a Lie algebra over a field K. The dual Lie coalgebra Lº of L has been defined by W. Michaelis to be the sum of all good subspaces V of the dual space L* of L: V is good if tm(V) ⊂ V ⊗ V, where m is the multiplication of L. We show that Lº = tm-1(L* ⊗ L*) as in the associative case.

On the doubling of quadratic algebras

Lars Lindberg (2004)

Colloquium Mathematicae

The concept of doubling, which was introduced around 1840 by Graves and Hamilton, associates with any quadratic algebra 𝓐 over a field k of characteristic not 2 its double 𝓥(𝓐 ) = 𝓐 × 𝓐 with multiplication (w,x)(y,z) = (wy - z̅x,xy̅ + zw). This yields an endofunctor on the category of all quadratic k-algebras which is faithful but not full. We study in which respect the division property of a quadratic k-algebra is preserved under doubling and, provided this is the case, whether the...

On the geometric prequantization of brackets.

Manuel de León, Juan Carlos Marrero, Edith Padrón (2001)

RACSAM

En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.

On the ghost centre of Lie superalgebras

Maria Gorelik (2000)

Annales de l'institut Fourier

We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.

On the homology of free Lie algebras

Calin Popescu (1998)

Commentationes Mathematicae Universitatis Carolinae

Given a principal ideal domain R of characteristic zero, containing 1 / 2 , and a connected differential non-negatively graded free finite type R -module V , we prove that the natural arrow 𝕃 F H ( V ) → F H 𝕃 ( V ) is an isomorphism of graded Lie algebras over R , and deduce thereby that the natural arrow U F H 𝕃 ( V ) → F H U 𝕃 ( V ) is an isomorphism of graded cocommutative Hopf algebras over R ; as usual, F stands for free part, H for homology, 𝕃 for free Lie algebra, and U for universal enveloping algebra. Related facts and examples are also considered....

Currently displaying 1261 – 1280 of 2676