On the structure of ternary Clifford algebras and their irreducible representations

DOI10.1007/s00006-021-01190-zzbMath1483.15015OpenAlexW4205709636MaRDI QIDQ2077413

Rafał Abłamowicz

Publication date: 21 February 2022

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-021-01190-z

zbMATH Keywords

irreducible representationcenterinvolutionopposite algebraprimitive idempotentcentral idempotentgraded algebra morphism\(\mathbb{Z}_3\)-graded algebraternary Clifford algebra

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Clifford algebras, spinors (15A66) Finite nilpotent groups, (p)-groups (20D15) Graded rings and modules (associative rings and algebras) (16W50)

Uses Software

• CLIFFORD
• Maple
• SymGroupAlgebra
• TernaryClifford

Cites Work

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• Spinor representations of Clifford algebras: A symbolic approach
• A classification of Clifford algebras as images of group algebras of Salingaros vee groups
• \(\mathbb{Z}_ 3\)-graded exterior differential calculus and gauge theories of higher order
• On ternary Clifford algebras on two generators defined by extra-special 3-groups of order 27
• Pseudo-inverses without matrices
• Ternary Clifford algebras
• Internal quark symmetries and colour \(\mathrm{SU}(3)\) entangled with \(Z_3\)-graded Lorentz algebra
• Hypersymmetry: A ℤ3-graded generalization of supersymmetry
• Ideals, Varieties, and Algorithms

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