Vol. 11, No. 5, 2018

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On the faithfulness of the representation of $\mathrm{GL}(n)$ on the space of curvature tensors

Corey Dunn, Darien Elderfield and Rory Martin-Hagemeyer

Vol. 11 (2018), No. 5, 775–785
Abstract

We prove that the standard representation of $GL\left(n\right)$ on the space of algebraic curvature tensors is almost faithful by showing that the kernel of this representation contains only the identity map and its negative. We additionally show that the standard representation of $GL\left(n\right)$ on the space of algebraic covariant derivative curvature tensors is faithful.

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Keywords
algebraic covariant derivative curvature tensor, algebraic curvature tensor, representation theory
Primary: 20G05
Secondary: 15A69