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(n) 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(n) on the space of algebraic covariant derivative curvature tensors is faithful.

Keywords
algebraic covariant derivative curvature tensor, algebraic curvature tensor, representation theory
Mathematical Subject Classification 2010
Primary: 20G05
Secondary: 15A69
Milestones
Received: 16 August 2016
Revised: 23 August 2017
Accepted: 29 October 2017
Published: 2 April 2018

Communicated by Kenneth S. Berenhaut
Authors
Corey Dunn
Mathematics Department
California State University at San Bernardino
San Bernardino, CA
United States
Darien Elderfield
Mathematics Department
North Carolina State University
Raleigh, NC
United States
Rory Martin-Hagemeyer
Mathematics Department
Rutgers University
Piscataway, NJ
United States