# A Simplicial Construction for Noncommutative Settings

## TL;DR

This paper introduces a new simplicial construction method to define higher Hochschild homology in noncommutative algebraic settings, expanding the tools available for studying such structures.

## Contribution

It presents a novel simplicial construction for higher Hochschild homology applicable to noncommutative algebras, broadening existing theoretical frameworks.

## Key findings

- The construction generalizes Hochschild homology to noncommutative contexts.
- Examples demonstrate the applicability of the construction to various algebraic structures.
- The approach provides new insights into noncommutative homological invariants.

## Abstract

In this paper we present a general construction that can be used to define the higher Hochschild homology for a noncommutative algebra. We also discuss other examples where this construction can be used.