3-split Casimir operator of the \(sl(M|N)\) and \(osp(M|N)\) simple Lie superalgebras in the representation \(\operatorname{ad}^{\otimes 3}\) and the vogel parameterization

DOI10.1134/S004057792410009XzbMATH Open1548.17014MaRDI QIDQ6632297

A. A. Provorov, A. P. Isaev

Publication date: 4 November 2024

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

invariant subspaceprojectorsimple Lie superalgebrasplit Casimir operatorVogel parameters

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Structure theory for Lie algebras and superalgebras (17B05)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra
• Gradings on walled Brauer algebras and Khovanov's arc algebra
• On universal knot polynomials
• Universality in Chern-Simons theory
• Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
• On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
• A universal dimension formula for complex simple Lie algebras
• On algebras which are connected with the semisimple continuous groups
• Casimir eigenvalues for universal Lie algebra
• OPERATOR INVARIANTS OF TANGLES, ANDR-MATRICES
• THE TENSOR ALGEBRA OF THE IDENTITY REPRESENTATION AS A MODULE OVER THE LIE SUPERALGEBRAS $ \mathfrak{Gl}(n,\,m)$ AND $ Q(n)$
• Braids, Link Polynomials and a New Algebra
• Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters
• On (ad)n(X2)k series of universal quantum dimensions
• Theory of Groups and Symmetries
• X ₂ series of universal quantum dimensions
• Lie superalgebras
• The split Casimir operator and solutions of the Yang-Baxter equation for the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters

This page was built for publication: 3-split Casimir operator of the \(sl(M|N)\) and \(osp(M|N)\) simple Lie superalgebras in the representation \(\operatorname{ad}^{\otimes 3}\) and the vogel parameterization

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6632297)