TL;DR
This paper studies the resolution quiver of connected Nakayama algebras, proving that all cycles are of equal size and weight, revealing uniformity in their structure.
Contribution
It establishes that all cycles in the resolution quiver of a connected Nakayama algebra are of the same size and weight, a new structural insight.
Findings
All cycles in the resolution quiver are of the same size.
All cycles in the resolution quiver have the same weight.
Abstract
Recently, Ringel introduced the resolution quiver for a connected Nakayama algebra. It is known that each connected component of the resolution quiver has a unique cycle. We prove that all cycles in the resolution quiver are of the same size. We introduce the notion of weight for a cycle in the resolution quiver. It turns out that all cycles have the same weight.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Quantum many-body systems