Higher Auslander algebras of type $\mathbb{A}$ and the higher Waldhausen $S$-constructions

Abstract

These notes are an expanded version of my talk at the ICRA 2018 in Prague, Czech Republic; they are based on joint work with Tobias Dyckerhoff and Tashi Walde. In them we relate Iyama's higher Auslander algebras of type $\mathbb{A}$ to Eilenberg--Mac Lane spaces in algebraic topology and to higher-dimensional versions of the Waldhausen $S$-construction from algebraic $K$-theory.

16 pages. The author's contribution to the Proceedings of the ICRA 2018, v.2 minor edits following referee report

References in corpus (5)

• Higher Nakayama algebras I: Construction
• Simplicial structures in higher Auslander-Reiten theory
• Higher Segal structures in algebraic $K$-theory
• Generalised BGP reflection functors via the Grothendieck construction
• The Grothendieck group of an n-angulated category