$\infty$-constructible Subsemigroups of $M_2(\mathbb{C})$

TL;DR

This paper characterizes all subsemigroups of 2x2 complex matrices that can be expressed as countable intersections of constructible sets, revealing their structure as intersections of constructible semigroups.

Contribution

It provides a complete description of $ abla$-constructible subsemigroups of $M_2(C)$ and shows they are intersections of constructible semigroups, advancing understanding of algebraic and geometric properties.

Findings

All $ abla$-constructible subsemigroups are characterized.

They are intersections of constructible semigroups.

The structure of these subsemigroups is explicitly described.

Abstract

A description of all subsemigroups of $M_2(\mathbb{C})$ which are given by a countable intersection of constructible sets is given. Furthermore, it is shown that they are intersections of constructible semigroups.