# Post-symmetric braces and integration of post-Lie algebras

## TL;DR

This paper introduces post-symmetric braces as a new algebraic structure related to post-Lie algebras, exploring their role in D-algebras and connections with the post-Lie Magnus expansion.

## Contribution

It defines post-symmetric braces, establishes their significance in post-Lie algebra theory, and links them to D-algebras and the Magnus expansion.

## Key findings

- Post-symmetric braces are identified as the analogue of symmetric brace algebras.
- Relations between post-symmetric braces and post-Lie Magnus expansion are established.
- The role of these structures in D-algebras is elucidated.

## Abstract

In this paper we identify the post-Lie analogue of the symmetric brace algebras, advocate their role in the theory of the associated D-algebras and present some relations with the so-called post-Lie Magnus expansion.