Standard Modules for Tabular Algebras

Annihilating Fields of Standard Modules for Affine Lie Algebras

Given an affine Kac-Moody Lie algebra g̃[σ] of arbitrary type, we determine certain minimal sets of annihilating fields of standard g̃[σ]-modules. We then use these sets in order to obtain a characterization of standard g̃[σ]modules in terms of irreducible loop g̃[σ]-modules, which proves to be a useful tool for combinatorial constructions of bases for standard g̃[σ]-modules.

Relations for Annihilating Fields of Standard Modules for Affine Lie Algebras

J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In a joint work with Arne Meurman this approach is developed further in the framework of vertex operator algebras. The main ingredients of that construction are defining relations for standard modules and relations...

Rees Algebras of Modules

We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allow the use of deformation theory. One can talk about the (essentially unique) Bourbaki ideal I(E) of a module E which, in many situations, allows to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Maca...

Operads, Algebras and Modules

There are many different types of algebra: associative, associative and commutative, Lie, Poisson, etc., etc. Each comes with an appropriate notion of a module. As is becoming more and more important in a variety of fields, it is often necessary to deal with algebras and modules of these sorts “up to homotopy”. I shall give a very partial overview, concentrating on algebra, but saying a little ...

Multiplicative bijective maps on standard operator algebras