# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1904.10163