On the structure of noncommutative mapping schemes

TL;DR

This paper explores the structure of noncommutative mapping schemes by examining ind-schemes of mappings and homomorphisms in the context of schemes, quantum groups, and Hopf algebras, using a dual functorial formalism.

Contribution

It introduces a dual functorial framework for analyzing ind-schemes of mappings and homomorphisms involving schemes and quantum groups, extending classical concepts to noncommutative settings.

Findings

Characterization of ind-schemes of mappings between schemes

Extension of the formalism to quantum groups and G-schemes

Framework for understanding noncommutative mapping schemes

Abstract

The following three types of objects are considered in a dual functorial formalism: (i) ind-scheme of mappings between two schemes, (ii) for a quantum group G, ind-scheme of G-mappings between two G-schemes, and (iii) ind-scheme of group homomorphisms between two quantum group. By schemes and quantum groups here we mean objects which are respectively dual to unital associative algebras and Hopf algebras.