Albert’s twisted field construction using division algebras with a multiplicative norm

Pumplün, Susanne

Abstract

We generalize Albert’s twisted field construction, applying it to unital division algebras with a multiplicative norm. We give conditions for the resulting algebras to be division algebras. Four- and eight-dimensional real unital and non-unital division algebras with large derivation algebras are constructed out of Hamilton’s quaternion and Cayley’s octonion algebra.

Citation

Pumplün, S. (2025). Albert’s twisted field construction using division algebras with a multiplicative norm. Journal of Algebra and Its Applications, 24(11), Article 2550253. https://doi.org/10.1142/S0219498825502536

• Journal Article Type: Article
• Acceptance Date: Mar 16, 2024
• Online Publication Date: Apr 26, 2024
• Publication Date: 2025-09
• Deposit Date: Mar 19, 2024
• Publicly Available Date: Apr 27, 2025
• Journal: Journal of Algebra and Its Applications
• Print ISSN: 0219-4988
• Electronic ISSN: 1793-6829
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 11
• Article Number: 2550253
• DOI: https://doi.org/10.1142/S0219498825502536
• Keywords: Real division algebras, Albert’s twisted fields, composition algebra
• Public URL: https://nottingham-repository.worktribe.com/output/32744190
• Publisher URL: https://www.worldscientific.com/doi/10.1142/S0219498825502536