Bachir Bekka

collaborators

3 papers

cond-mat.mtrl-sci2025

Representations of the symmetry groups of infinite crystals

Bachir Bekka, Christian Brouder

We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with perio…

math.RT2025

Canonical Commutation Relations: A quick proof of the Stone-von Neumann theorem and an extension to general rings

Bachir Bekka

Let $R$ be a (not necessary commutative) ring with unit, $d \geq 1$ an integer, and $I^»$ a unitary character of the additive group $(R, +) .$ A pair $(U, V)$ of unitary representations…

math.RT2024

The $L_{p}$ -dual space of a semisimple Lie group

Bachir Bekka

Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_{p}$ -spaces for $p \in (1, + \infty)$ with $p \neq = 2.$ More precisely, we…

Representations of the symmetry groups of infinite crystals

Canonical Commutation Relations: A quick proof of the Stone-von Neumann theorem and an extension to general rings

The Lp​-dual space of a semisimple Lie group

The $L_{p}$ -dual space of a semisimple Lie group