Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential rel ...
Let K be a global field of characteristic not 2. The embedding problem for maximal tori in a classical group G can be described in terms of algebras with involution. The aim of this paper is to give an explicit description of the obstruction group to the H ...
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...
In this thesis we are interested in the following problem : given two differential k–forms g and f, most of the time they will be assumed closed, on what conditions can we pullback g to f by a map φ ? In other words we ask when it is possible to solve the ...
We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra. ...
Let G be a finite group and (K, O, k) be a p-modular system “large enough”. Let R = O or k. There is a bijection between the blocks of the group algebra RG and the central primitive idempotents (the blocks) of the so-called cohomological Mackey algebra coμ ...
This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...
Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cance ...
Let A be a d-dimensional smooth algebra over a perfect field of characteristic not 2. Let Um(n+1)(A)/En+1 (A) be the set of unimodular rows of length n + 1 up to elementary transformations. If n >= (d + 2)/2, it carries a natural structure of group as disc ...
The starting point for this project is the article of Kathryn Hess [11]. In this article, a homotopic version of monadic descent is developed. In the classical setting, one constructs a category D(𝕋) of coalgebras in the Eilenberg-Moore category of ...
