Factorization of Symplectic Matrices into Elementary Factors

Björn Ivarsson; Frank Kutzschebauch; Erik Løw

doi:10.1090/proc/14891

Factorization of Symplectic Matrices into Elementary Factors

Björn Ivarsson, Frank Kutzschebauch, Erik Løw

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Abstract

We prove that a symplectic matrix with entries in a ring with Bass stable rank one can be factored as a product of elementary symplectic matrices. This also holds for null-homotopic symplectic matrices with entries in a Banach algebra or in the ring of complex valued continuous functions on a finite dimensional normal topological space.

Original language	English
Pages (from-to)	1963-1970
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	5
Early online date	2019
DOIs	https://doi.org/10.1090/proc/14891
Publication status	Published - May 2020
MoE publication type	A1 Journal article-refereed

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title = "Factorization of Symplectic Matrices into Elementary Factors",

abstract = "We prove that a symplectic matrix with entries in a ring with Bass stable rank one can be factored as a product of elementary symplectic matrices. This also holds for null-homotopic symplectic matrices with entries in a Banach algebra or in the ring of complex valued continuous functions on a finite dimensional normal topological space. ",

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AB - We prove that a symplectic matrix with entries in a ring with Bass stable rank one can be factored as a product of elementary symplectic matrices. This also holds for null-homotopic symplectic matrices with entries in a Banach algebra or in the ring of complex valued continuous functions on a finite dimensional normal topological space.

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JO - Proceedings of the American Mathematical Society

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Factorization of Symplectic Matrices into Elementary Factors

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