In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.
In this note, we study formal deformations of derived representations of the principal series representations of . In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for .
La théorie de M. Sato et T. Shintani associe à toute forme réelle d’un espace préhomogène irréductible régulier dont le groupe est réductif, une fonction zêta qui vérifie une équation fonctionnelle remarquable. Dans cet article, nous classifions les formes réelles infinitésimales des espaces préhomogènes irréductibles de type parabolique. Cette classification est obtenue en termes de diagrammes de Satake à poids.
First, we provide an introduction to the theory and algorithms for noncommutative Gröbner bases for ideals in free associative algebras. Second, we explain how to construct universal associative envelopes for nonassociative structures defined by multilinear operations. Third, we extend the work of Elgendy (2012) for nonassociative structures on the 2-dimensional simple associative triple system to the 4- and 6-dimensional systems.
We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...