Some Remarks on the Braided Thompson Group BV

TL;DR

This paper explores properties of the braided Thompson group BV, highlighting its potential for cryptography and demonstrating that it does not have non-trivial linear representations.

Contribution

It provides new insights into the algebraic properties of BV, especially its resistance to linear representations, which is relevant for cryptographic applications.

Findings

BV does not admit a non-trivial linear representation

Highlights potential cryptographic relevance of BV

Provides analysis of algebraic properties of BV

Abstract

Matthew Brin and Patrick Dehornoy independently discovered a braided version BV of Thompson's group V. In this paper, we discuss some properties of BV that might make the group interesting for group based cryptography. In particular, we show that BV does not admit a non-trivial linear representation.