The algebras of semi-invariants of euclidean quivers
Cristina Di Trapano
TL;DR
This paper provides a concise proof of the structure of semi-invariant algebras for Euclidean quivers without oriented cycles, building on existing generator results and properties of Schofield semi-invariants.
Contribution
It offers a new, shorter proof of Skowronski and Weyman's theorem using Derksen and Weyman's generator results and Schofield semi-invariants.
Findings
Simplified proof of the algebra structure
Clarified the role of Schofield semi-invariants
Extended understanding of Euclidean quivers
Abstract
We give a new short proof of Skowronski and Weyman's theorem about the structure of the algebras of semi-invariants of Euclidean quivers, in the case of quivers without oriented cycles. Our proof is based essentially on Derksen and Weyman's result about the generators of these algebras and properties of Schofield semi-invariants.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics