Albert's twisted field construction using division algebras with a\n multiplicative norm

2015/04/01 by Susanne Pumpluen, Pumpluen, Susanne
Mathematics · #17A35 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1504.00188

openalex publication_date 2015/04/01 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

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

Related

• About division quaternion algebras and division symbol algebras
• Algebres non associatives normees de division. Classification des algebres reelles de Jordan non commutatives de division lineaire de dimension 8
• About split quaternion algebras over quadratic fields and symbol algebras of degree n
• Division algebras that generalize Dickson semifields
• Division algebras, Galois fields, quadratic residues