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arXiv · 2403.05142

On matrix Lie affgebras

Tomasz Brzeziński·Krzysztof Radziszewski
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Abstract

Lie brackets or Lie affgebra structures on several classes of affine spaces of matrices are studied. These include general normalised affine matrices, special normalised affine matrices, anti-symmetric and anti-hermitian normalised affine matrices and special anti-hermitian normalised affine matrices. It is shown that, when retracted to the underlying vector spaces, they correspond to classical matrix Lie algebras: general and special linear, anti-symmetric, anti-hermitian and special anti-hermitian Lie algebras respectively.

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Tomasz Brzeziński, Krzysztof Radziszewski. 2024-03-08. On matrix Lie affgebras. https://arxiv.org/abs/2403.05142

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