arXiv subjects

Stephen Humphries

Publications and source records attributed to Stephen Humphries.

2 recordsLinked to original sources

arXiv2016

Points with finite orbits for trace maps

We study an action of ${\rm Aut}(F_n)$ on $\mathbb{R}^{2^n-1}$ by trace maps, defined using the traces of $n$-tuples of matrices in $\mathrm{SL}(2,\mathbb{C})$ having real traces. We determine the finite orbits for this action. These orbits essentially come from (i) the finite subgroups of $\mathrm{SL}(2,\mathbb C)$, and (ii) a dense set of (rational) points in an embedded quotient of an $n$-torus.

math.DS↗

arXiv2004

Trace identities from identities for determinants

We present new identities for determinants of matrices $(A_{i,j})$ with entries $A_{i,j}$ equal to $a_{i,j}$ or $a_{i,0}a_{0,j}-a_{i,j}$, where the $a_{i,j}$'s are indeterminates. We show that these identities are behind trace identities for $SL(2,\Bbb C)$ matrices found earlier by Magnus in his study of trace algebras.

math.AC↗