Infinite Dimensional Maximal Torus Revisited

Infinite Dimensional Maximal Torus Revisited

Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mi>m</mi></msup></semantics></math></inline-formula> be the maximal torus of a set of <inli...

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Bibliographic Details
Main Authors:	Mohamed Lemine H. Bouleryah, Akram Ali, Piscoran Laurian-Ioan
Format:	Article
Language:	English
Published:	MDPI AG 2024-12-01
Series:	Mathematics
Subjects:	measure-preserving transformations symplectic geometry moment map
Online Access:	https://www.mdpi.com/2227-7390/12/23/3829
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Summary:	Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mi>m</mi></msup></semantics></math></inline-formula> be the maximal torus of a set of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>×</mo><mi>m</mi></mrow></semantics></math></inline-formula> unitary diagonal matrices. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">T</mi></semantics></math></inline-formula> be a collection of all maps that rigidly rotate every circle of latitude of the sphere with a fixed angle. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">T</mi></semantics></math></inline-formula> is also a maximal torus, and we shall prove in this paper that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">T</mi></semantics></math></inline-formula> is the topological limit inf of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mi>m</mi></msup></semantics></math></inline-formula>.
ISSN:	2227-7390