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Displaying 1341 – 1360 of 2676

Operads for $n$ -ary algebras – calculations and conjectures

Martin Markl, Elisabeth Remm (2011)

Archivum Mathematicum

In [8] we studied Koszulity of a family ${t 𝒜 𝑠𝑠}_{d}^{n}$ of operads depending on a natural number $n \in ℕ$ and on the degree $d \in ℤ$ of the generating operation. While we proved that, for $n \leq 7$ , the operad ${t 𝒜 𝑠𝑠}_{d}^{n}$ is Koszul if and only if $d$ is even, and while it follows from [4] that ${t 𝒜 𝑠𝑠}_{d}^{n}$ is Koszul for $d$ even and arbitrary $n$ , the (non)Koszulity of ${t 𝒜 𝑠𝑠}_{d}^{n}$ for $d$ odd and $n \geq 8$ remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.

Operads of decorated trees and their duals

Vsevolod Yu. Gubarev, Pavel S. Kolesnikov (2014)

Commentationes Mathematicae Universitatis Carolinae

This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform...

Opérateurs différentiels bi-invariants

Mustapha Raïs (1976/1977)

Séminaire Bourbaki

Operateurs differentiels de Shimura et espaces prehomogenes.

H. Rubenthaler, G. Schiffmann (1987)

Inventiones mathematicae

Opérateurs différentiels et mesures invariantes

Jean-Yves Charbonnel (1993)

Compositio Mathematica

Operations for modules on Lie-Rinehart superalgebras.

Sophie Chemla (1995)

Manuscripta mathematica

Operator-valued Bessel functions on Jordan algebras.

Hongming Ding, Kenneth I. Gross (1993)

Journal für die reine und angewandte Mathematik

Orbit functions.

Klimyk, Anatoliy, Patera, Jiri (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Orbit measures, random matrix theory and interlaced determinantal processes

Manon Defosseux (2010)

Annales de l'I.H.P. Probabilités et statistiques

A connection between representation of compact groups and some invariant ensembles of hermitian matrices is described. We focus on two types of invariant ensembles which extend the gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant probability measures on adjoint orbits of a compact Lie group. These measures are described by semiclassical approximation involving tensor and restriction multiplicities. We show that a large class of them are determinantal....