Compression of bounded complexes and Auslander-Reiten sequences.

CLAUDIA CHAIO, ALFREDO GONZALEZ CHAIO E ISABEL PRATTI; MARIA JOSE SOUTO SALORIO

Madrid

Congreso; 25th Conference of the international Linear Algebra Soc. Madrid; 2023

Let A be a finite dimensional algebra with finite globaldimension. In [6], we found a link between the category ofperiodic complexes and the Happel’s root category usingthe compression functor. Related to these ideas, in [3] and[4] the authors describe the almost split sequences forperiodic complexes, in the case that A is a hereditaryalgebra. In this talk, we present some propertiesconcerning the compression functor of bounded complexesover a more general context. In particular, we prove thatit preserve indecomposable complexes and irreduciblemorphisms. The covering notion given in [1] and thecomplexes of fixed size studied in [2] will play a relevantrole in our work.