Locally coalgebra-Galois extensions

TL;DR

This paper introduces locally coalgebra-Galois extensions, explores conditions for their global counterparts, and demonstrates their application in constructing quantum lens spaces by gluing locally cleft extensions.

Contribution

It defines locally coalgebra-Galois extensions, establishes criteria for their global extension, and applies these concepts to quantum space constructions.

Findings

Conditions for local to global coalgebra-Galois extensions are established.

Gluing of locally cleft extensions yields global coalgebra-Galois extensions.

Quantum lens space constructed via gluing quantum solid tori.

Abstract

The paper introduces the notion of a locally coalgebra-Galois extension and, as its special case, a locally cleft extension. The necessary and sufficient conditions for a locally coalgebra-Galois extension to be a (global) coalgebra-Galois extension are stated. As an important special case, it is proven, that under not very restrictive conditions the gluing of two locally cleft extensions is a globally coalgebra-Galois extension. As an example, the quantum lens space of positive charge is constructed by gluing of two quantum solid tori.