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

TL;DR

This paper explores the connections between higher Auslander algebras of type A, algebraic topology, and higher-dimensional Waldhausen S-constructions, revealing new relationships in algebraic K-theory.

Contribution

It establishes a novel link between higher Auslander algebras and topological constructions like Eilenberg–Mac Lane spaces and higher Waldhausen S-constructions.

Findings

Relates higher Auslander algebras to Eilenberg–Mac Lane spaces

Connects algebraic K-theory with higher-dimensional Waldhausen constructions

Provides new insights into the structure of higher algebraic objects

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 $\operatorname{S}$-construction from algebraic $K$-theory.