Cyclic division algebras and maximal tori
Yao-Rui Yeo
TL;DR
This paper links the cardinality of a specific nonabelian cohomology related to cyclic division algebras to partition numbers, providing insights into the conjugacy classes of maximal tori over abelian extensions.
Contribution
It establishes a novel connection between nonabelian cohomology of cyclic division algebras and combinatorial partition numbers, aiding the classification of maximal tori.
Findings
Cardinality of nonabelian cohomology equals a partition number
Interpretation of conjugacy classes of maximal tori over abelian extensions
New computational approach for cohomology in algebraic structures
Abstract
We show the cardinality of a particular nonabelian cohomology associated to cyclic division algebras is equal to a certain partition number. This computation helps us interpret the number of conjugacy classes of maximal tori defined over an abelian extension.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology