Conjugacy Classes of Subalgebras of the Real Sedenions
Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 492-507
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By applying the Cayley–Dickson process to the division algebra of real octonions, one obtains a 16-dimensional real algebra known as (real) sedenions. We denote this algebra by ${{\text{A}}_{4}}$ . It is a flexible quadratic algebra (with unit element 1) but not a division algebra.We classify the subalgebras of ${{\text{A}}_{4}}$ up to conjugacy (i.e., up to the action of the automorphism group $G$ of ${{\text{A}}_{4}}$ ) with one exception: we leave aside the more complicated case of classifying the quaternion subalgebras. Any nonzero subalgebra contains 1 and we show that there are no proper subalgebras of dimension 5, 7 or > 8. The proper non-division subalgebras have dimensions 3, 6 and 8. We show that in each of these dimensions there is exactly one conjugacy class of such subalgebras. There are infinitely many conjugacy classes of subalgebras in dimensions 2 and 4, but only 4 conjugacy classes in dimension 8.
Chan, Kai-Cheong; Đoković, Dragomir Ž. Conjugacy Classes of Subalgebras of the Real Sedenions. Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 492-507. doi: 10.4153/CMB-2006-048-6
@article{10_4153_CMB_2006_048_6,
author = {Chan, Kai-Cheong and {\DJ}okovi\'c, Dragomir \v{Z}.},
title = {Conjugacy {Classes} of {Subalgebras} of the {Real} {Sedenions}},
journal = {Canadian mathematical bulletin},
pages = {492--507},
year = {2006},
volume = {49},
number = {4},
doi = {10.4153/CMB-2006-048-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-048-6/}
}
TY - JOUR AU - Chan, Kai-Cheong AU - Đoković, Dragomir Ž. TI - Conjugacy Classes of Subalgebras of the Real Sedenions JO - Canadian mathematical bulletin PY - 2006 SP - 492 EP - 507 VL - 49 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-048-6/ DO - 10.4153/CMB-2006-048-6 ID - 10_4153_CMB_2006_048_6 ER -
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