Generation of the symplectic group by involutions

Ellers, Erich W.; Villa, Oliver

doi:10.1016/j.laa.2020.01.003

Linear Algebra and its Applications

2020

DOI: 10.1016/j.laa.2020.01.003

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Generation of the symplectic group by involutions

Erich W. Ellers

Oliver Villa

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Cited by 6 publications

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“…In 1981, Gow proved that if char F = 2, then every symplectic matrix over F is a product of two symplectic involutions [8]. In 2020, Ellers and Villa showed that every symplectic matrix over F of size at least 4 is a product of 6 or fewer symplectic involutions provided −1 is a square in F [6].…”

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confidence: 99%

Products of skew-involutions

Joven

Paras

2023

ELA

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It is shown that every $2n$-by-$2n$ matrix over a field $\mathbb{F}$ with determinant 1 is a product of (i) four or fewer skew-involutions ($A^2 = -I$) provided $\mathbb{F} \neq \mathbb{Z}_3$, and (ii) eight or fewer skew-involutions if $\mathbb{F} = \mathbb{Z}_3$ and $n > 1$. Every real symplectic matrix is a product of six real symplectic skew-involutions, and an explicit factorization of a complex symplectic matrix into two symplectic skew-involutions is given.

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confidence: 99%

Products of skew-involutions

Joven

Paras

2023

ELA

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Products of two involutions in orthogonal and symplectic groups

de Seguins Pazzis

2023

Geom Dedicata

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Reality of unipotent elements in classical Lie groups

Gongopadhyay¹,

Maity²

2023

Bulletin des Sciences Mathématiques

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Generation of the symplectic group by involutions

Cited by 6 publications

References 3 publications

Products of skew-involutions

Products of skew-involutions

Products of two involutions in orthogonal and symplectic groups

Reality of unipotent elements in classical Lie groups

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