A Family of surjective word map on SU(2)

TL;DR

This paper investigates the surjectivity of a specific family of word maps on the special unitary group SU(2), contributing to understanding how algebraic words influence group element coverage.

Contribution

It introduces a new family of words in the free group and analyzes their surjectivity on SU(2), revealing novel properties of word maps in this context.

Findings

Identifies conditions under which the word map is surjective on SU(2)

Provides examples of words with specific surjectivity properties

Enhances understanding of algebraic structure of SU(2) related to free group words

Abstract

Let $\mathbf{F}$ be the free group on two generators $a, b$ and let a family of words $w = [[a, b], [a^3, b^n]]$ in $\mathbf{F}$. In this paper we examine surjectivity of word map $w$ on special unitary group SU(2) over complex field $\mathbf{C}$.