Perfect Derived Categories of Positively Graded DG Algebras

2008/09/27 by Olaf M. Schnürer, Schnürer, Olaf M.
Mathematics · Physics and Astronomy · #16D90 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0809.4782

openalex publication_date 2008/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the perfect derived category dgPer(A) of a positively graded differential graded (dg) algebra A whose degree zero part is a dg subalgebra and semisimple as a ring. We introduce an equivalent subcategory of dgPer(A) whose objects are easy to describe, define a t-structure on dgPer(A) and study its heart. We show that dgPer(A) is a Krull-Remak-Schmidt category. Then we consider the heart in the case that A is a Koszul ring with differential zero satisfying some finiteness conditions.

Related

• Reflexive dg categories in algebra and topology
• The Differential Graded Stable Category of a Self-Injective Algebra
• Koszul differential graded algebras and BGG correspondence
• Differential graded division algebras, their modules, and dg-simple algebras
• Weight structures and simple dg modules for positive dg algebras