Modularität und Distributivität im Subidealverband einer Lie-Algebra
Dans cet article, on classifie les modules de plus haut poids unitarisables sur la super-algèbre de Virasoro tordue.
With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let be such a group. The stack of all representations of dimension is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack which is better behaved, and, in particular, admits a coarse algebraic space, which...
Motivated by the two dimensional conformal field theory with gauge symmetry, we shall study the monodromy of the integrable connections associated with the simple Lie algebras. This gives a series of linear representations of the braid group whose explicit form is described by solutions of the quantum Yang-Baxter equation.
This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms...
Since the mid-nineties it has gradually become understood that the Cartan prolongation of rank 2 distributions is a key operation leading locally, when applied many times, to all so-called Goursat distributions. That is those, whose derived flag of consecutive Lie squares is a 1-flag (growing in ranks always by 1). We first observe that successive generalized Cartan prolongations (gCp) of rank k + 1 distributions lead locally to all special k-flags: rank k + 1 distributions D with the derived...
Let be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to -tuples of commuting finite order automorphisms. It is a classical result that is the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in . In this paper, we classify the algebras in , and further determine the relationship between and two...