Trace identities from identities for determinants

Abstract

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 $SL(2,\mathbb{C})$ matrices found earlier by Magnus in his study of trace algebras.

14 pages, AmS-TeX