Complexes de Koszul quantiques

Generalized Koszul Complexes

This article should be viewed as a survey of generalized Koszul complexes and Koszul bicomplexes with an application to generalized Koszul complexes in projective dimension one. We shall try to give detailed information on the basic definitions and a summary of the main results. Concerning proofs the reader is invited to have a look into [I] or [IV]. Introduction. We start with the following qu...

A Remark on Koszul Complexes

j j mj m b mj mi for all m mi M When M is a nite free R module then the vanishing of the homology of K is determined by the grade g of the ideal Im one hasHj K for j n g n and Hn g K Giving a linear form on a nite free R module of rank n is equivalent to specifying a sequence a an of elements of R If M is not a free R module then the picture changes drastically In this note we investigate the s...

Computing the Homology of Koszul Complexes

Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each f. g. projective R/I-module V has an Rprojective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P1 → P0 for all n ≥ 1, if d = 1. This computation yields a new proof of the classical Adams-Riemann-R...

Diagrammes De Temperley-lieb Colorés Et Groupes Quantiques

On rencontre les diagrammes de Temperley-Lieb dans des contextes variés. 1. Topologie du plan : par définition. 2. Abstraction : on peut définir avec générateurs et relations des structures du genre algèbres, catégories etc. et puis montrer que ce sont les mêmes que celles obtenues sur les diagrammes de Temperley-Lieb en faisant des opérations topologiques. 3. Algèbre : les axiomes des algèbres...

LASERS A BLOCAGE DE MODES A BASE DE BATONNETS QUANTIQUES InAs/InP POUR LES COMMUNICATIONS OPTIQUES