On, around, and beyond Frobenius' theorem on division algebras

DOI10.1080/03081087.2020.1761281zbMath1489.16014arXiv1912.07846OpenAlexW3026676140MaRDI QIDQ5073034

Matej Brešar, Viktor S. Shul'man

Publication date: 5 May 2022

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.07846

zbMATH Keywords

quaternionsdivision algebrafinite-dimensional algebraFrobenius' theoremWedderburn's principal theoremliftable roots

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Finite-dimensional division rings (16K20) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Cites Work

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• Lifting algebraic elements in \(C^*\)-algebras
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• Exchange rings, exchange equations, and lifting properties
• On the parallelizability of the spheres
• NON-PARALLELIZABILITY OF THE n-SPHERE FOR n > 7
• Lifting Idempotents and Exchange Rings
• Semiprojectivity of universal $C^{*}$-algebras generated by algebraic elements

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