Abstract

We show that there is no nontrivial group homomorphism [Formula: see text] over commutative local rings and division rings for [Formula: see text], respectively. It gives a negative answer to Ye’s problem (see [S. K. Ye, Low-dimensional representations of matrix group actions on CAT(0) spaces and manifolds, J. Algebra 409 (2014) 219–243]) for the above rings.

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