Quantum Symmetries: From Clifford and Hurwitz Algebras to M-Theory and Leech Lattices

Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent

doi:10.1007/s00006-018-0894-3

Cited by 10 publications

(5 citation statements)

References 17 publications

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“…Octonions also describe geometry in 10 dimensions [5], which have made them useful in supergravity and superstring theories [6,7,8,9]. Recently there has been a revived interest in using the division algebras to attempt to construct a theoretical basis for the observed Standard Model (SM) gauge groups and observed particle spectrum [10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Gillard

Gresnigt

2019

Eur. Phys. J. C

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We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry SU (3) c × U (1) em can be described using the algebra of complexified sedenions C ⊗ S. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of C ⊗ S can be used to uniquely split the algebra into three complex octonion subalgebras C ⊗ O. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 C-dimensional C ⊗ O subalgebras on themselves generates three copies of the Clifford algebra C (6). It was previously shown that the minimal left ideals of C (6) describe a single generation of fermions with unbroken SU (3) c × U (1) em gauge symmetry. Extending this construction from C ⊗ O to C ⊗ S naturally leads to a description of exactly three generations.

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Section: Introductionmentioning

confidence: 99%

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Gillard

Gresnigt

2019

Eur. Phys. J. C

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“…The Jacobi identity do not hold, since [ , [ , ]] = − 7 ̸ = 0, where 7 anticommutes with and * . The algebra of split octonions is crucial for the suppression of unwanted states and is fully discussed in our papers [25][26][27] in detail. The automorphism group of the algebra is just SU(3) .…”

Section: Color Algebra and Octonionsmentioning

confidence: 99%

Effective Hadronic Supersymmetry from Quantum Chromodynamics

et al. 2019

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“…We had shown [1,2] that the algebra of octonions neatly represented hadronic supersymmetry based on the extension of the spin-flavor group SU (6) to the supergroup SU (6/21). In considering a rotationally excited baryon (qqq), the most energetically stable configuration occurs when two of the quarks come together at a point to form a diquark (D = qq) on one end of a spherical bag structure leaving the remaining quark (q) on the opposite end.…”

Section: Introductionmentioning

confidence: 99%

Characterization of New Algebras Resembling Colour Algebras based on Split-Octonion units in the Classification of Hadronic Symmetries and Supersymmetries

Burdik,

Catto,

Gürcan

et al. 2023

J. Phys.: Conf. Ser.

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We report on some new algebras we discovered that does not appear in mathematics or physics literature which we briefly name “R” algebras. Together with the real forms we developed for supersting theories shown below and dobbed as “l” algebras, both these new algebras seem to imitate split-octonionic multiplication rules we expose below. We further elaborate on Jordan algebras, magic squares, seven spheres, and supergravity, pointing to the existence of a larger theory with a 27-dimensional lattice and unifying all known superstring theories.

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Quantum Symmetries: From Clifford and Hurwitz Algebras to M-Theory and Leech Lattices

Cited by 10 publications

References 17 publications

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Effective Hadronic Supersymmetry from Quantum Chromodynamics

Characterization of New Algebras Resembling Colour Algebras based on Split-Octonion units in the Classification of Hadronic Symmetries and Supersymmetries

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