Mapping spaces and automorphism groups of toric noncommutative spaces

TL;DR

This paper introduces a sheaf-theoretic framework for toric noncommutative geometry, enabling the formalization of mapping spaces and automorphism groups, with a focus on their algebraic structures.

Contribution

It develops a sheaf theory approach to define and analyze mapping spaces and automorphism groups in toric noncommutative geometry, providing new algebraic insights.

Findings

Mapping spaces between toric noncommutative spaces are formalized.

Automorphism groups' Lie algebra is described via braided derivations.

The approach offers a new perspective on symmetries in noncommutative geometry.

Abstract

We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application we study the `internalized' automorphism group of a toric noncommutative space and show that its Lie algebra has an elementary description in terms of braided derivations.