# Multi-switches and representations of braid groups

## TL;DR

This paper introduces the concept of multi-switches to construct new algebraic representations of virtual braid groups, extending previous methods and broadening the understanding of braid group representations.

## Contribution

It generalizes the notion of switches to multi-switches and provides a new framework for constructing braid group representations using automorphisms.

## Key findings

- New representations of virtual braid groups introduced
- Generalized several known braid group representations
- Provided a systematic approach for constructing algebraic representations

## Abstract

In the paper, we introduce the notion of a (virtual) multi-switch which generalizes the notion of a (virtual) switch. Using (virtual) multi-switches we introduce a general approach on how to construct representations of (virtual) braid groups by automorphisms of algebraic systems. As a corollary, we introduce new representations of virtual braid groups which generalize several previously known representations.