Simple roots of deformed preprojective algebras
Lieven Le Bruyn
TL;DR
This paper offers alternative descriptions for the dimension vectors of simple representations of deformed preprojective algebras, building on Crawley-Boevey's work but relying on quotient variety irreducibility.
Contribution
It provides new descriptions of simple representation dimension vectors, expanding understanding beyond Crawley-Boevey's original characterization.
Findings
Alternative descriptions depend on quotient variety irreducibility
Descriptions do not simplify the proof of Crawley-Boevey's result
Highlights limitations of current methods in the theory of deformed preprojective algebras
Abstract
W. Crawley-Boevey has given a description of the set of dimension vectors of simple representations of the deformed preprojective algebras. In this note we give alternative descriptions. Note however that our descriptions depend on irreducibility of the quotient varieties, so they do NOT give a shorter proof of Crawley-Boevey's result.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons