Displaying 201 – 220 of 1857

Showing per page

Calogero-Moser spaces and an adelic W -algebra

Emil Horozov (2005)

Annales de l’institut Fourier

We introduce a Lie algebra, which we call adelic W -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.

Canonical bases for 𝔰𝔩 ( 2 , ) -modules of spherical monogenics in dimension 3

Roman Lávička (2010)

Archivum Mathematicum

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as 𝔰𝔩 ( 2 , ) -modules. As finite-dimensional irreducible 𝔰𝔩 ( 2 , ) -modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.

Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann

Alain Connes (1974)

Annales de l'institut Fourier

Nous démontrons que la catégorie de von Neumann est équivalente à la catégorie des cônes autopolaires, facialement homogènes, complexes. Un cône dans un espace hilbertien réel est dit : 1) facialement homogène quand pour toute face F de l’opérateur δ = (Projection sur F - F ) - (Projection sur F - F ) est une dérivation de (i.e. e t δ = t R ) ; 2) complexe quand on s’est donné une structure d’algèbre de Lie complexe sur l’algèbre de Lie réelle des dérivations de , modulo son centre. Nous caractérisons les espaces...

Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.

Sergio A. Albeverio, Ayupov, Shavkat, A. 2, Bakhrom A. Omirov (2006)

Revista Matemática Complutense

In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan s criterion of solvability is proved.

Category 𝒪 for quantum groups

Henning Haahr Andersen, Volodymyr Mazorchuk (2015)

Journal of the European Mathematical Society

In this paper we study the BGG-categories 𝒪 q associated to quantum groups. We prove that many properties of the ordinary BGG-category 𝒪 for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for 𝒪 and for finite dimensional U q -modules we are able to determine...

Characteristic homomorphism for ( F 1 , F 2 ) -foliated bundles over subfoliated manifolds

José Manuel Carballés (1984)

Annales de l'institut Fourier

In this paper a construction of characteristic classes for a subfoliation ( F 1 , F 2 ) is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of ( F 1 , F 2 ) -foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of F i -foliated bundles, i = 1 , 2 , the results of Kamber-Tondeur on the cohomology of g - D G -algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation...

Characteristic zero loop space homology for certain two-cones

Calin Popescu (1999)

Commentationes Mathematicae Universitatis Carolinae

Given a principal ideal domain R of characteristic zero, containing 1/2, and a two-cone X of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra F H ( Ω X ; R ) to be isomorphic with the universal enveloping algebra of some R -free graded Lie algebra; as usual, F stands for free part, H for homology, and Ω for the Moore loop space functor.

Currently displaying 201 – 220 of 1857