Parafermions for higher order extensions of the Poincaré algebra and their associated superspace

Abstract

Parafermions of order two and three are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincaré algebra. The corresponding superfields are constructed, and some of their main properties analyzed in detail. In this context, the existence problem of operators acting like covariant derivatives is analyzed, and the associated operators are explicitly constructed.

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References in corpus (6)

• Modeling Multiple M2's
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Poincaré and sl(2) algebras of order 3
• Ternary algebras and groups
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Cited by in corpus (5)

• n-ary algebras: a review with applications
• The partially alternating ternary sum in an associative dialgebra
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• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework