منابع مشابه
Conway’s group and octonions
We give a description of the double cover of Conway’s group in terms of right multiplications by 3× 3 matrices over the octonions. This leads to simple sets of generators for many of the maximal subgroups, including a uniform construction of the Suzuki chain of subgroups.
متن کاملSpinors and Octonions
Octonions are introduced through some spin representations. The groups G2, F4 and the E series appear in a natural manner; one way to understand octonions is as the “second coming” of the reals, but with the spinors instead of vectors. Some physical applications in M and F -theory as putative “theories of everything” are suggested. 1 The Seven Sphere . Consider the real, complex and quaternion ...
متن کاملTfHE OCTONIONS
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon thei...
متن کاملOctonions and M-theory
We explain how structures related to octonions are ubiquitous in M theory. All the exceptional Lie groups, and the projective Cayley line and plane appear in M -theory. Exceptional G2-holonomy manifolds show up as compactifying spaces, and are related to the M2 Brane and 3-form. We review this evidence, which comes from the initial 11-dim structures. Relations between these objects are stressed...
متن کاملQuaternions and Octonions in Mechanics
In fact, this group is Spin(3), the 2-fold cover of SO(3), the group of rotations of R. This has been known for quite some time and is perhaps the simplest realization of Hamilton’s expectations about the potential of quaternions for physics. One reason for the renewed interest is the fact that the resulting substitution of matrices by quaternions speeds up considerably the numerical calculatio...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2021
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2021.122006