-structure on the Cohomology of the Free 2-Nilpotent Lie Algebra
Calcolo della funzione di partizione di Kostant
Forniamo un calcolo esplicito della funzione di partizione di Kostant per algebre di Lie complesse di rango . La tecnica principale consiste nella riduzione a casi più semplici ed all'uso di funzioni generatrici.
Calculating canonical distinguished involutions in the affine Weyl groups.
Calculations with the Temperley - Lieb algebra.
Calogero-Moser spaces and an adelic -algebra
We introduce a Lie algebra, which we call adelic -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.
Canonic inference and commutative orthogonal block structure
It is shown how to define the canonic formulation for orthogonal models associated to commutative Jordan algebras. This canonic formulation is then used to carry out inference. The case of models with commutative orthogonal block structures is stressed out.
Canonical bases for -modules of spherical monogenics in dimension 3
Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as -modules. As finite-dimensional irreducible -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.
Canonical realizations of Lie algebras associated with foliated coadjoint orbits
Capelli elements for the orthogonal Lie algebras.
Capelli identities for Lie superalgebras
Caractères d'algèbres de Lie finies
Caractères semi-simples de , corps local non archimédien
Soit un corps local non archimédien de caractéristique résiduelle différente de et . Nous définissons strates semi-simples et caractères semi-simples pour le groupe exceptionnel à l’aide des objets analogues pour le groupe , des automorphismes de trialité et d’une correspondance de Glauberman. Nous construisons alors les types semi-simples associés et nous donnons des conditions suffisantes pour que ces types s’induisent irréductiblement, obtenant ainsi des représentations supercuspidales...
Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann
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 de l’opérateur (Projection sur ) (Projection sur ) est une dérivation de (i.e. ) ; 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.
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.
Cartan-Involution von halbeinfachen reellen Jordan-Tripelsystemen.
Casimir operators on pseudodifferential operators of several variables.
Categories of nonstandard highest weight modules for affine Lie algebras.
Category for quantum groups
In this paper we study the BGG-categories associated to quantum groups. We prove that many properties of the ordinary BGG-category for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when 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 and for finite dimensional -modules we are able to determine...
Cayley-Dickson Construction
Cayley-Dickson construction produces a sequence of normed algebras over real numbers. Its consequent applications result in complex numbers, quaternions, octonions, etc. In this paper we formalize the construction and prove its basic properties.
Cells of harmonicity
[For the entire collection see Zbl 0742.00067.]We are interested in partial differential equations on domains in . One of the most natural questions is that of analytic continuation of solutions and domains of holomorphy. Our aim is to describe the domains of holomorphy for solutions of the complex Laplace and Dirac equations. We call them cells of harmonicity. We deduce their properties mostly by examining geometrical properties of the characteristic surface (which is the same for both equations),...