Weyl tensors, strongly regular graphs, multiplicative characters, and a quadratic matrix equation

We study solutions of a quadratic matrix equation arising in Riemannian geometry. Let S be a real symmetric n×n-matrix with zeros on the diagonal and let θ be a real number. We construct nonzero solutions (S,θ) of the set of quadratic equations∑kSi,k=0 and ∑kSi,kSk,j+Si,j2=θSi,j for i

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Bibliographic Details
Published in:Journal of algebra 2024-10, Vol.656, p.170-195
Main Authors: Deninger, Christopher, Grundhöfer, Theo, Kramer, Linus
Format: Article
Language:English
Subjects:
curvature tensors
group rings
multiplicative characters
Ricci flow
strongly regular graphs
Weyl tensors
Citations: Items that this one cites
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Description
Summary:We study solutions of a quadratic matrix equation arising in Riemannian geometry. Let S be a real symmetric n×n-matrix with zeros on the diagonal and let θ be a real number. We construct nonzero solutions (S,θ) of the set of quadratic equations∑kSi,k=0 and ∑kSi,kSk,j+Si,j2=θSi,j for i
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2023.08.028