Characteristic polynomials of central simple algebras
Chia-Fu Yu
TL;DR
This paper characterizes the characteristic polynomials of elements in central simple algebras, extending classical linear algebra concepts to non-commutative algebraic structures.
Contribution
It provides a comprehensive characterization of characteristic polynomials in central simple algebras and develops the theory of rational canonical forms in this context.
Findings
Characterization of characteristic polynomials in central simple algebras
Development of rational canonical forms for separable transformations
Description of separable conjugacy classes in the multiplicative group
Abstract
We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description of separable conjugacy classes of the multiplicative group.
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Taxonomy
TopicsAdvanced Topics in Algebra · Polynomial and algebraic computation · Matrix Theory and Algorithms