42 citations · 84 across the 10 of their papers we have counts for
11 papers
Commutation relations of and the incidence geometry of the Fano plane
Michel Rausch de Traubenberg, M J Slupinski
We continue our study and classification of structures on the Fano plane and its dual involved in the construction of octonions and the Lie algebra $\mat…
Incidence geometry of the Fano plane and Freudenthal's ansatz for the construction of (split) octonions
Michel Rausch de Traubenberg, Marcus J. Slupinski
In this article we consider structures on a Fano plane which allow a generalisation of Freudenthal's construction of a norm and a bilinear multiplication law on an eight…
Pure spinors and a construction of the -Lie algebras
Marcus Slupinski, Robert Stanton
Let be a -dimensional hyperbolic space and its Clifford algebra. has a -grading, , and an algebra isomorphism , $…
Polynomial invariants and moduli of generic two-dimensional commutative algebras
M. Rausch de Traubenberg, M. Slupinski
Let be a two-dimensional vector space over a field of characteristic not or . We show there is a canonical surjection from the set of suitably generic co…
The geometry of special symplectic representations
Marcus J. Slupinski, Robert J. Stanton
We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties…
The special symplectic structure of binary cubics
Marcus Slupinski, Robert J. Stanton
Let be a field of characteristic not 2 or 3. Let be the -space of binary cubic polynomials. The natural symplectic structure on promotes to a symplectic structure…
Finite-dimensional Lie subalgebras of the Weyl algebra
M. Rausch de Traubenberg, M. J. Slupinski, A. Tanasa
We classify up to isomorphism all finite-dimensional Lie algebras that can be realised as Lie subalgebras of the complex Weyl algebra . The list we obtain turns out to be disc…
Finite-dimensional Lie algebras of order F
M. Rausch de Traubenberg, M. J. Slupinski
Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). When not many finite-dimensional examples are known. In this paper we construc…
Fractional Supersymmetry and F-fold Lie Superalgebras
M. Rausch de Traubenberg, M. J. Slupinski
We give infinite dimensional and finite dimensional examples of fold Lie superalgebras. The finite dimensional examples are obtained by an inductive procedure from Lie algebras…
Kac-Moody algebras and Lie algebras of regular vector fields on tori
M. Rausch de Traubenberg, M. J. Slupinski
We consider the problem of representing the Kac-Moody algebra specified by an indecomposable generalised Cartan matrix as vector fields on the tor…
Fractional Supersymmetry and Fth-Roots of Representations
M. Rausch de Traubenberg, M. J. Slupinski
A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorp…