Several Results Concerning Convex Subcategories

TL;DR

This paper explores the properties of convex subcategories across various algebra classes, analyzing factor algebras formed by specific ideals to deepen understanding of their structural relationships.

Contribution

It extends the concept of convex subcategories to a broad spectrum of algebra classes and investigates their factor algebras, providing new insights into their structural properties.

Findings

Convex subcategories apply to many algebra classes.

Factor algebras generated by idempotents retain convexity properties.

Results unify understanding of algebra structures through convex subcategories.

Abstract

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In particular, given an algebra $\Lambda$ from one of the aforementioned classes, we investigate certain factor algebras $\Lambda/I$ where $I$ is an ideal generated by a suitable idempotent.