Matrix representation of octonions and generalizations
نویسندگان
چکیده
منابع مشابه
Clifford algebra-parametrized octonions and generalizations
Introducing products between multivectors of Cl0,7 (the Clifford algebra over the metric vector space R) and octonions, resulting in an octonion, and leading to the non-associative standard octonionic product in a particular case, we generalize the octonionic X-product, associated with the transformation rules for bosonic and fermionic fields on the tangent bundle over the 7-sphere S, and the X...
متن کاملMatrix Representations of Octonions and Their Applications
As is well-known, the real quaternion division algebra H is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra O can not be algebraically isomorphic to any matrix algebras over the real number field R, because O is a non-associative algebra over R. However since O is an extension of H by the Cayley-Dickson process and is also finite-dimensional, som...
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The Leech lattice, Λ24, is represented on the space of octonionic 3vectors. It is built from two octonionic representations of E8, and is reached via Λ16. It is invariant under the octonion index cycling and doubling maps. supported in part by alien invaders.
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jedoch noch nicht hergeleitet werden. Abstract In this thesis generalizations of matrix and eigenvalue models involving supersym-metry are discussed. Following a brief review of the Hermitian one matrix model, the c = −2 matrix model is considered. Built from a matrix valued superfield this model displays supersymmetry on the matrix level. We stress the emergence of a Nicolai–map of this model ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1999
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532950