Complete order isomorphisms between Non-Commutative $L^2$-spaces.

Maps between Non-commutative Spaces

Let J be a graded ideal in a not necessarily commutative graded k-algebra A = A0⊕A1⊕· · · in which dimk Ai <∞ for all i. We show that the map A→ A/J induces a closed immersion i : Projnc A/J → Projnc A between the non-commutative projective spaces with homogeneous coordinate rings A and A/J . We also examine two other kinds of maps between non-commutative spaces. First, a homomorphism φ : A → B...

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 ...

Geometric non commutative phase spaces

The aim of this paper is to describe some geometric examples of non commutative and cyclic phase spaces, filling a gap in the literature and developing the project of geometrization of semantics for linear logics started in [12]. Besides, we present an algebraic semantics for non commutative linear logic with exponentials.

Subspaces of Non-commutative Spaces

This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a non-commutative space.