Philippe Meyer

activity

20172020

collaborators

6 papers

math.RT2020

Symplectic Dirac operators for Lie algebras and graded Hecke algebras

Dan Ciubotaru, Marcelo De Martino, Philippe Meyer

We define a pair of symplectic Dirac operators $(D^{+}, D^{-})$ in an algebraic setting motivated by the analogy with the algebraic orthogonal Dirac operators in representation theory.…

math.RT2020

Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras

Philippe Meyer

The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition to construct a colour Lie algebra from an $ε$ -orthogo…

math.RT2020

Geometric properties of special orthogonal representations associated to exceptional Lie superalgebras

Philippe Meyer

From an octonion algebra $O$ over a field $k$ of characteristic not two or three, we show that the fundamental representation $Im (O)$ of the derivation alge…

math.RA2020

Involutions of sl(2,k) and non-split, three-dimensional simple Lie algebras

Philippe Meyer

We give a process to construct non-split, three-dimensional simple Lie algebras from involutions of sl(2,k), where k is a field of characteristic not two. Up to equivalence, non-sp…

math.RT2019

The Kostant invariant and special $ε$ -orthogonal representations for $ε$ -quadratic colour Lie algebras

Philippe Meyer

Let k be a field of characteristic not two or three, let $g$ be a finite-dimensional colour Lie algebra and let V be a finite-dimensional representation of $\mathfrak{g}…

math.RT2017

Classification of finite-dimensional Lie superalgebras whose even part is a three-dimensional simple Lie algebra over a field of characteristic not two or three

Philippe Meyer

Let $k$ be a field of characteristic not two or three. We classify up to isomorphism all finite-dimensional Lie superalgebras $g = g_{0} \oplus g_{1}$ ove…

Symplectic Dirac operators for Lie algebras and graded Hecke algebras

Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras

Geometric properties of special orthogonal representations associated to exceptional Lie superalgebras

Involutions of sl(2,k) and non-split, three-dimensional simple Lie algebras

The Kostant invariant and special ε-orthogonal representations for ε-quadratic colour Lie algebras

Classification of finite-dimensional Lie superalgebras whose even part is a three-dimensional simple Lie algebra over a field of characteristic not two or three

The Kostant invariant and special $ε$ -orthogonal representations for $ε$ -quadratic colour Lie algebras