2015/06/08 by Alexander Zimmermann, Zimmermann, Alexander
Computer Science · Mathematics · Medicine · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Categorical variable #Degeneration (medical) #Epistemology #FOS: Mathematics #Mathematics #Medicine #Pathology #Philosophy #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Sociology #Statistics #Topological and Geometric Data Analysis #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1506.02393
47th Symposiu, on Ring Theory and Representation Theory, Sep 2014, Osaka, Japan. Proceedings of the 47th Symposium on Ring Theory and Representation Theory September 13-15, 2014; Saitama University February 2015
arxiv created 2015/06/08 · openalex publication_date 2015/06/08 · arxiv updated 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety and isomorphism classes correspond to orbits under this action. A module M degenerates to a module N if N belongs to the Zariski closure of the orbit of M. Yoshino gave a scheme-theoretic characterisation, and Saorin and Zimmermann generalise this concept to general triangulated categories. We show that this concept has an interpretation in terms of distinguished triangles, analogous to the Riedtmann-Zwara characterisation for modules. In this manuscript we report on these results and study the behaviour of this degeneration concept under functors between triangulated categories.