Permutahedra, HKR isomorphism and polydifferential Gerstenhaber-Schack complex

TL;DR

This paper introduces the theory of props, properads, dioperads, and operads, illustrating their connection to permutahedra and simplicial complexes, and explores applications to Hochschild-Kostant-Rosenberg isomorphisms.

Contribution

It provides a self-contained introduction to these algebraic structures and offers a prop(erad)ic interpretation of permutahedra with applications to Hochschild-Kostant-Rosenberg isomorphisms.

Findings

Prop(erad)ic interpretation of permutahedra

Application to Hochschild-Kostant-Rosenberg isomorphisms

Introduction to (wheeled) props, properads, dioperads, operads

Abstract

This paper aims to give a short but self-contained introduction into the theory of (wheeled) props, properads, dioperads and operads, and illustrate some of its key ideas in terms of a prop(erad)ic interpretation of simplicial and permutahedra cell complexes with subsequent applications to the Hochschild-Kostant-Rosenberg type isomorphisms.