On the classification of the real flexible division algebras

• Autorzy: Erik Darpö
• Języki publikacji: EN

Abstrakty

EN

We investigate the class of finite-dimensional real flexible division algebras.
We classify the commutative division algebras, completing an approach by Althoen and Kugler. We solve the isomorphism problem for scalar isotopes of quadratic division algebras, and classify the generalised pseudo-octonion algebras. In view of earlier results by Benkart, Britten and Osborn and Cuenca Mira et al., this reduces the problem of classifying the real flexible division algebras to the normal form problem of the action of the group 𝒢₂ by conjugation on the set of positive definite symmetric linear endomorphisms of ℝ⁷. A method leading to the solution of this problem is demonstrated.
In addition, the automorphism groups of the real flexible division algebras are described.

Kategorie tematyczne

• 15A21: Canonical forms, reductions, classification
• 17A20: Flexible algebras
• 17A45: Quadratic algebras (but not quadratic Jordan algebras)
• 17A36: Automorphisms, derivations, other operators
• 17A35: Division algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 105
• Numer: 1
• Strony: 1-17

Daty

wydano

2006

Twórcy

autor

Erik Darpö

• Matematiska Institutionen, Uppsala Universitet, Box 480, S-75106 Uppsala, Sweden

Identyfikatory

DOI

10.4064/cm105-1-1