Generalised Split Octonions and their transformation in SO(7) symmetry
K. Pushpa, P. S. Bisht, O. P. S. Negi
TL;DR
This paper introduces a novel approach to describing SO(7) symmetry transformations using generalized split octonions, extending the algebraic framework beyond traditional matrix representations.
Contribution
It presents a new formulation of SO(8) generators via generalized split octonions and applies them to describe SO(7) rotational transformations.
Findings
Generators of SO(8) expressed with split octonions
Application to SO(7) vector transformations
Extension of algebraic methods for symmetry groups
Abstract
Generators of SO(8) group have been described by using direct product of the Gamma matrices and the Pauli Sigma matrices. We have obtained these generators in terms of generalized split octonion also. These generators have been used to describe the rotational transformation of vectors for SO(7) symmetry group.
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