Connected gradings and fundamental group

Abstract

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we study the relation between gradings and Galois coverings. This theoretical tool gives information about the fundamental group of $A$, which allows its computation using complete lists of gradings.

Final version to appear in Algebra & Number Theory. 26 pages

References in corpus (1)

• The universal cover of an algebra without double bypass

Cited by in corpus (4)

• The Intrinsic Fundamental Group of a Linear Category
• On weak equivalences of gradings
• The fundamental group of a Hopf linear category
• Full and convex linear subcategories are incompressible