Algebras of block Toeplitz matrices with commuting entries
Muhammad Ahsan Khan, Dan Timotin
TL;DR
This paper investigates the structure of maximal algebras of block Toeplitz matrices with entries from a commutative algebra, extending known results from scalar to block cases and classifying specific maximal algebras.
Contribution
It provides a classification of maximal algebras of block Toeplitz matrices with commuting entries, advancing understanding beyond scalar cases.
Findings
Classified all maximal algebras for certain commutative algebras
Extended scalar Toeplitz algebra results to block matrices
Identified structural properties of block Toeplitz algebras
Abstract
The maximal algebras of scalar Toeplitz matrices are known to be formed by generalized circulants. The identification of algebras consisting of block Toeplitz matrices is a harder problem, that has received little attention up to now. We consider the case when the block entries of the matrices belong to a commutative algebra . After obtaining some general results, we classify all the maximal algebras for certain particular cases of .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms