Asymptotic Grothendieck groups and c.b.l.f. positive dgalgebras
Abstract
We introduce the notion of asymptotic Grothendieck groups for abelian and triangulated categories that are both AB4 and AB4*. We study when the asymptotic Grothendieck group of the heart of a triangulated category with a tstructure is isomorphic to the asymptotic Grothendieck group of the triangulated category itself. We also explain a connexion with the notion of topological Grothendieck group from AcharStroppel. Finally, we compute the asymptotic Grothendieck group of some positive (dg)algebras having a cone bounded, locally finite dimension.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1906.07215
 arXiv:
 arXiv:1906.07215
 Bibcode:
 2019arXiv190607215N
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Representation Theory
 EPrint:
 v2, 66pages, with additional examples