In algebra, an Okubo algebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by Susumu Okubo.[1] Okubo algebras are composition algebras, flexible algebras (A(BA) = (AB)A), Lie admissible algebras, and power associative, but are not associative, not alternative algebras, and do not have an identity element.
Okubo's example was the algebra of 3-by-3 trace-zero complex matrices, with the product of X and Y given by aXY + bYX – Tr(XY)I/3 where I is the identity matrix and a and b satisfy a + b = 3ab = 1. The Hermitian elements form an 8-dimensional real non-associative division algebra. A similar construction works for any cubic alternative separable algebra over a field containing a primitive cube root of unity. An Okubo algebra is an algebra constructed in this way from the trace-zero elements of a degree-3 central simple algebra over a field.[2]
^Susumu Okubo (1978)
^Max-Albert Knus, Alexander Merkurjev, Markus Rost, Jean-Pierre Tignol (1998) "Composition and Triality", chapter 8 in The Book of Involutions, pp 451–511, Colloquium Publications v 44, American Mathematical Society ISBN 0-8218-0904-0
In algebra, an Okuboalgebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by Susumu Okubo. Okubo algebras...
the group of rotations of the E8 lattice. G2 manifold Octonion algebraOkuboalgebra Spin(7) manifold Spin(8) Split-octonions Triality Sabadini, Irene;...
of nonassociative algebras are flexible: Alternative algebras Lie algebras Jordan algebras (which are commutative) Okuboalgebras Similarly, the following...
non-associative) and even non-alternative flexible algebras like the sedenions and Okuboalgebras. Any algebra whose elements are idempotent is also power-associative...
Susumu Okubo (大久保 進, Ōkubo Susumu, 2 March 1930 – July 17, 2015) was a Japanese theoretical physicist at the University of Rochester. Ōkubo worked primarily...
algebra under the product a ∘ b = ab + ba. Malcev-admissible algebra Lie-admissible algebraOkubo 1995, pp. 19, 84 Albert, A. Adrian (1948), "Power-associative...
ISBN 0-8218-1095-2. MR 2104929. Zbl 1068.11023. Okubo, Susumu (1995). Introduction to octonion and other non-associative algebras in physics. Montroll Memorial Lecture...
important role in K-theory for C*-algebras and in the Murray-von Neumann theory of projections in a von Neumann algebra. Any orthogonal projection is one...
Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras. Cambridge University Press. p. 148. ISBN 978-0521079884. Bonsall, F.;...
flavor quantum numbers, invisible to the strong interactions. The Gell-Mann–Okubo mass formula systematized the quantification of these small mass differences...
93d2128M. doi:10.1103/PhysRevE.93.042128. PMID 27176275. S2CID 206249608. Okubo, S.; M. Hayashi; S. Kimura; H. Ohta; M. Motokawa; H. Kikuchi; H. Nagasawa...
illustrator and screen-printer associated with the San Francisco Renaissance Miné Okubo (1912–2001), Nisei, painter, author of Citizen 13660, her book documenting...
"Changes" Changes (single) Rhythm Zone Kenichi Maeyamada CHI-MEY Kaoru Okubo CM song for Triumph’s Tenshi No Bra 2008-10-29 Milky Way "Tan Tan Taan!"...
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