Search results for "Pure Mathematics"

Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized surfaces

2014

The module structure of Hochschild homology in some examples

2008

Abstract In this Note we give a simple proof of a conjecture by A. Caldararu stating the compatibility between the modified Hochschild–Kostant–Rosenberg isomorphism and the action of Hochschild cohomology on Hochschild homology in the case of Calabi–Yau manifolds and smooth projective curves. To cite this article: E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

2006

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.

Representations of modules over a*-algebra and related seminorms

2008

Representations of a module X over a � -algebra A# are considered and some related seminorms are constructed and studied, with the aim of finding bounded � -representations of A #.

Partial {$*$}-algebras of closable operators. II. States and representations of partial {$*$}-algebras

1991

This second paper on partial Op*-algebras is devoted to the theory of representations. A new definition of invariant positive sesquilinear forms on partial *-algebras is proposed, which enables to perform the familiar GNS construction. In order to get a better control of the corresponding representations, we introduce and study a restricted class of partial Op*-algebras, called partial GW*-algebras, which turn up naturally in a number of problems. As an example, we extend Powers' results about the standardness of GNS representations of abelian partial *-algebras.

Sui gruppi unitari finitari e sulla congettura di dieudonné

1996

In this paper we consider some questions concerning unitary spaces (V, h), even though (V, h) is not finitely generated.

Cohomologie relative des applications polynomiales

2001

Let F be a polynomial dominating mapping from Cn to Cq with n>q. We study the de Rham cohomology of the fibres of F, and its relative cohomology groups. Let us fix a strictly positive weighted homogeneous degree on C[x1,…,xn]. With the leading terms of the coordinate functions of F, we construct a fibre of F that is said to be “at infinity”. We introduce the cohomology groups of F at infinity. These groups, denoted by Hk(F−1(∞)), enable us to study all the other cohomology groups of F. For instance, if the fibre at infinity has an isolated singularity at the origin, we prove that any quasi-homogeneous basis of Hn−q(F−1(∞)) provides a basis of all groups Hn−q(F−1(y)), as well as a basis of t…

Banach elements and spectrum in Banach quasi *-algebras

2006

A normal Banach quasi -algebra (X;A_0) has a distinguished Banach - algebra X_b consisting of bounded elements of X. The latter -algebra is shown to coincide with the set of elements of X having fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).

Codimension growth of special simple Jordan algebras

2009

Let $R$ be a special simple Jordan algebra over a field of characteristic zero. We exhibit a noncommutative Jordan polynomial $f$ multialternating on disjoint sets of variables which is not a polynomial identity of $R$. We then study the growth of the polynomial identities of the Jordan algebra $R$ through an analysis of its sequence of Jordan codimensions. By exploiting the basic properties of the polynomials $f$, we are able to compute the exponential rate of growth of the sequence of Jordan codimensions of $R$ and prove that it equals the dimension of the Jordan algebra over its center. We also show that for any finite dimensional special Jordan algebra, such exponential rate of growth c…

A Lattice-Geometric Proof of Wedderburn’s Theorem

1993

This note presents a proof of Wedderburn’s theorem concerning the classification of semisimple rings within the conceptual frame of projective lattice geometry.