2015/09/11 by William Crawley-Boevey, Crawley-Boevey, William, Julia Sauter +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Endomorphism #Endomorphism ring #Injective function #Injective module #Mathematics #Orbit (dynamics) #Projective representation #Projective test #Pure mathematics #Quiver #Quotient #Representation (politics) #Ring (chemistry) #math.RT #msc:14L30 #msc:14M15 #msc:16G60
paper · pdf · doi:10.48550/arxiv.1509.03460
Section 4 split into two, and a characterization of the projective quotient algebra (Theorem 5.6) added
openalex publication_date 2015/09/11 · arxiv created 2015/09/28 · arxiv updated 2015/09/29 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/06
We show that Auslander algebras have a unique tilting and cotilting module\nwhich is generated and cogenerated by a projective-injective; its endomorphism\nring is called the projective quotient algebra. For any representation-finite\nalgebra, we use the projective quotient algebra to construct desingularizations\nof quiver Grassmannians, orbit closures in representation varieties, and their\ndesingularizations. This generalizes results of Cerulli Irelli, Feigin and\nReineke.\n