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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
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Abstract |
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We prove that the standard representation of 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 on the space of algebraic covariant derivative curvature tensors is faithful. |
Keywords
algebraic covariant derivative curvature tensor, algebraic
curvature tensor, representation theory
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Mathematical Subject Classification 2010
Primary: 20G05
Secondary: 15A69
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Milestones
Received: 16 August 2016
Revised: 23 August 2017
Accepted: 29 October 2017
Published: 2 April 2018
Communicated by Kenneth S. Berenhaut
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Authors |
| Corey Dunn | |
| Mathematics Department California State University at San Bernardino San Bernardino, CA United States |
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| Darien Elderfield | |
| Mathematics Department North Carolina State University Raleigh, NC United States |
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| Rory Martin-Hagemeyer | |
| Mathematics Department Rutgers University Piscataway, NJ United States |
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