On Asymptotic Reducibility in SL(3,Z)
Oleg Karpenkov
TL;DR
This paper explores the reducibility properties of Hessenberg matrices in SL(3,Z), focusing on matrices with one real and two complex conjugate eigenvalues, advancing understanding of their conjugacy class representations.
Contribution
It investigates the specific case of Hessenberg matrices with mixed eigenvalue types in SL(3,Z), addressing an open problem in the field.
Findings
Characterization of reducibility for matrices with complex eigenvalues
Identification of conditions affecting conjugacy class representations
Extension of previous Hessenberg matrix representations in SL(n,Z)
Abstract
Recently we showed that Hessenberg matrices are proper to represent conjugacy classes in SL(n,Z). In this paper we focus on the reducibility properties in the set of Hessenberg matrices of SL(3,Z). We investigate the first interesting open case here: the case of matrices having one real and two complex conjugate eigenvalues.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Advanced Topics in Algebra