ON THE CLASSIFICATION OF $4$ -DIMENSIONAL QUADRATIC DIVISION ALGEBRAS OVER SQUARE-ORDERED FIELDS

DOI10.1112/S0024610701003064zbMath1017.17004MaRDI QIDQ3151101

Ernst Dieterich, Johan Öhman

Publication date: 22 October 2002

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

classificationconfigurationmatrix pair problemquadratic division algebradissident triplesquare-ordered field

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Finite-dimensional division rings (16K20) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22) Nonassociative division algebras (17A35) Quadratic algebras (but not quadratic Jordan algebras) (17A45)

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Real commutative division algebras ⋮ The double sign of a real division algebra of finite dimension greater than one ⋮ The algebraic and geometric classification of transposed Poisson algebras ⋮ Exhaustive construction of four-dimensional unital division algebras over finite fields with Kleinian automorphism group ⋮ Von-Neumann finiteness and reversibility in some classes of non-associative algebras ⋮ Duplication methods for embeddings of real division algebras ⋮ The degree of an eight-dimensional real quadratic division algebra is 1, 3, or 5 ⋮ CLASSIFICATION, AUTOMORPHISM GROUPS AND CATEGORICAL STRUCTURE OF THE TWO-DIMENSIONAL REAL DIVISION ALGEBRAS ⋮ Trace Invariants of Finite-Dimensional Algebras ⋮ The algebraic classification of nilpotent commutative algebras ⋮ Liftings of dissident maps

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