On the classification of the real flexible division algebras

Erik Darpö. "On the classification of the real flexible division algebras." Colloquium Mathematicae 105.1 (2006): 1-17. <http://eudml.org/doc/286458>.

@article{ErikDarpö2006,
abstract = { 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. },
author = {Erik Darpö},
journal = {Colloquium Mathematicae},
keywords = {real division algebra; flexible algebra; scalar isotope; generalized pseudo-octonion algebra; commutative algebra; automorphism; group action},
language = {eng},
number = {1},
pages = {1-17},
title = {On the classification of the real flexible division algebras},
url = {http://eudml.org/doc/286458},
volume = {105},
year = {2006},
}

TY - JOUR
AU - Erik Darpö
TI - On the classification of the real flexible division algebras
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 1
SP - 1
EP - 17
AB - 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.
LA - eng
KW - real division algebra; flexible algebra; scalar isotope; generalized pseudo-octonion algebra; commutative algebra; automorphism; group action
UR - http://eudml.org/doc/286458
ER -