Warianty tytułu
Języki publikacji
Abstrakty
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.
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-17
Opis fizyczny
Daty
wydano
2006
Twórcy
autor
- Matematiska Institutionen, Uppsala Universitet, Box 480, S-75106 Uppsala, Sweden
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-1