On characteristic equations, trace identities and Casimir operators of simple Lie algebras

DOI10.1063/1.533300zbMath0985.17005arXivmath-ph/9907024OpenAlexW1966239502MaRDI QIDQ2738002

Hendryk Pfeiffer, Alan J. Macfarlane

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/math-ph/9907024

zbMATH Keywords

trace relationsnonprimitive Casimir operatorstensorial Lie relations

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Simple, semisimple, reductive (super)algebras (17B20)

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Cites Work

• Okubo's quartic trace formula for exceptional Lie algebras
• The geometry of compact Lie groups
• Higher-order simple Lie algebras
• Invariant tensors for simple groups
• Modified fourth-order Casimir invariants and indices for simple Lie algebras
• Characteristic identities for semi-simple Lie algebras
• Simple Groups and Strong Interaction Symmetries
• Symmetric power sum expansions of the eigenvalues of generalised Casimir operators of semi-simple Lie groups
• Casimir invariants and vector operators in simple and classical Lie algebras
• Quartic trace identity for exceptional Lie algebras
• An explicit construction of Casimir operators and eigenvalues. II
• Invariant tensors and Casimir operators for simple compact Lie groups
• Matrix Products and the Explicit 3, 6, 9, and 12-j Coefficients of the Regular Representation of SU(n)
• Characteristic Identities for Generators of GL(n), O(n) and Sp(n)
• Identity satisfied by the d-type coefficients of SU(n)

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