Identities with coefficients in simple compact Lie groups

Michael Larsen; Aner Shalev

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arXiv · 2208.07418

Identities with coefficients in simple compact Lie groups

Michael Larsen·Aner Shalev

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Abstract

We conjecture that if $G$ is a simple compact Lie group with trivial center, then every $d$-variable non-constant word map with coefficients in $G$ defines a non-constant function on $G^d$. We prove the conjecture for $A_r$, $B_r$, $E_6$, and $G_2$ using a ping-pong argument.

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Michael Larsen, Aner Shalev. 2022-08-15. Identities with coefficients in simple compact Lie groups. https://arxiv.org/abs/2208.07418

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