Every Gabriel quiver of an algebra of generalized quaternion type reduces to a finite tame periodicity shadow, with all 2-cycles confined to a small list of local blocks.
Local structure of tame symmetric algebras of period four
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e. the numbers of arrows starting and ending at any vertex are equal, and do not exceed $2$. We describe the local structure of biregular Gabriel quivers of tame symmetric algebras of period four, including certain idempotent algebras. The main result of this paper shows that, in fact, these Gabriel quivers have local structure exactly as Gabriel quivers of so called {\it weighted surface algebras}, which partially extends known characterization of algebras of generalized quaternion type.
fields
math.RT 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Periodicity shadows I: A new approach to combinatorics of periodic algebras
Every Gabriel quiver of an algebra of generalized quaternion type reduces to a finite tame periodicity shadow, with all 2-cycles confined to a small list of local blocks.