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Subgroups of Clifford algebras
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Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on these groups and algebras may suggest ways in which they might be applied more widely to describe the fundamental properties of matter. I do not claim to build a physical theory on top of the fundamental algebra, and my suggestions for possible physical interpretations are indicative only, and may not work. Nevertheless, both the existence of three generations of fermions and the symmetry-breaking of the weak interaction seem to emerge naturally from an extension of the Dirac algebra from complex numbers to quaternions.
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Cited by 2 Pith papers
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Sharp Lower Bound on the Minimax Risk for Multinomial Uniformity Testing via a Conditional Central Limit Theorem
The multinomial minimax risk for uniformity testing against $l_p$ alternatives converges exactly to $2Phi(-u^*/2)$ in the intermediate regime, proven via a conditional central limit theorem.
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A Superalgebra Within: representations of lightest standard model particles form a $\mathbb{Z}_2^5$-graded algebra
Standard Model particle representations (minus top-quark irreps) are shown to fit into a Z2^5-graded Jordan superalgebra H_16(C) generated by division algebras.
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