Parastatistics as Lie-supertriple systems

DOI10.1063/1.530486zbMath0832.17032arXivhep-th/9312180OpenAlexW2093806710MaRDI QIDQ4314253

Susumu Okubo

Publication date: 5 March 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9312180

zbMATH Keywords

Lie superalgebrasparastatisticsbosonic and fermionic operatorsLie- supertriple system

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Ternary compositions (17A40)

Related Items (16)

QUASI-CLASSICAL LIE SUPERALGEBRAS AND LIE SUPERTRIPLE SYSTEMS ⋮ Centroids of Lie supertriple systems ⋮ Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras ⋮ Jacobson generators of the quantum superalgebra Uq[sl(n+1|m) and Fock representations] ⋮ Jacobson generators, Fock representations and statistics of sl(n+1) ⋮ 1-parameter formal deformations, Nijenhuis operators and abelian extensions of \(\delta\)-Lie color triple systems ⋮ 1-parameter formal deformations and abelian extensions of Lie color triple systems ⋮ Many-body Wigner quantum systems ⋮ k-Leibniz algebras from lower order ones: From Lie triple to Lie ℓ-ple systems ⋮ On Killing forms and invariant forms of Lie-Yamaguti superalgebras ⋮ Supergeneralization of Duffin–Kemmer–Petiau Algebra and Lie superalgebra osp(N,M) ⋮ Enveloping Lie superalgebras and Killing-Ricci forms of Bol superalgebras ⋮ Highest weight irreducible representations of the Lie superalgebra gl(1|∞) ⋮ Derivations and deformations of \(\delta\)-Jordan Lie supertriple systems ⋮ Topics in isotopic pairs and their representations. II: The general supercase ⋮ A classification of generalized quantum statistics associated with basic classical Lie superalgebras

Cites Work

• A structure theory of Freudenthal-Kantor triple systems
• Fermi-Bose Similarity
• Triple products and Yang–Baxter equation. I. Octonionic and quaternionic triple systems
• Wigner approach to quantization. Noncanonical quantization of two particles interacting via a harmonic potential
• Lie superalgebras

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