Twisting non-commutative L spaces

Embeddings of Non-commutative L P -spaces in Non-commutative L 1 -spaces, 1 < P < 2

It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomor-phic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative L p (N;)-spaces deened by a semi-nite, normal, faithful trace on a von Neumann algebra N. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting.

Integral Non - Commutative Spaces

Integral Non-commutative Spaces

A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module EX such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of EX . A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative ...

EMBEDDINGS OF NON - COMMUTATIVE Lp - SPACES INTO NON - COMMUTATIVE L 1 - SPACES , 1 < p < 2 Marius Junge

It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative Lp(N, τ)-spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting. Introduction and Notation The theory of p-stab...

Twisting Commutative Algebraic Groups

If V is a commutative algebraic group over a field k, O is a commutative ring that acts on V , and I is a finitely generated free O-module with a right action of the absolute Galois group of k, then there is a commutative algebraic group I ⊗O V over k, which is a twist of a power of V . These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori...