A Calabi-Yau algebra with $E_6$ symmetry and the Clebsch-Gordan series of $sl(3)$

zbMath1490.17018arXiv2005.13444MaRDI QIDQ5034858

Nicolas Crampé, Luc Vinet, Loïc Poulain d'Andecy

Publication date: 21 February 2022

Full work available at URL: https://arxiv.org/abs/2005.13444

zbMATH Keywords

Calabi-Yau algebraClebsch-Gordan seriescentraliser algebraHeun operatorspolarised tracesWeyl group of type \(E_6\)

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Semisimple Lie groups and their representations (22E46) Universal enveloping algebras of Lie algebras (16S30)

Related Items (4)

Generalized quadratic commutator algebras of PBW-type ⋮ Chern-Simons theory, link invariants and the Askey-Wilson algebra ⋮ The missing label of \(\mathfrak{su}_3\) and its symmetry ⋮ Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Superintegrability in two dimensions and the Racah-Wilson algebra
• Noncommutative del Pezzo surfaces and Calabi-Yau algebras
• Poincaré-Birkhoff-Witt deformations of Calabi-Yau algebras.
• A Lie-theoretic construction of spherical symplectic reflection algebras
• The diamond lemma for ring theory
• The invariant theory of \(n\times n\) matrices
• Algebraic Heun operator and band-time limiting
• The ring of generic matrices.
• Denominators for the Poincaré series of invariants of small matrices
• The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type
• Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products.
• Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials
• Clebsch-Gordan coefficients of SU(3) with simple symmetry properties
• TRACE IDENTITIES OF FULL MATRIX ALGEBRAS OVER A FIELD OF CHARACTERISTIC ZERO
• Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
• Temperley–Lieb, Brauer and Racah algebras and other centralizers of 𝔰𝔲(2)
• The Heun–Racah and Heun–Bannai–Ito algebras
• The Heun operator of Hahn-type

This page was built for publication: A Calabi-Yau algebra with $E_6$ symmetry and the Clebsch-Gordan series of $sl(3)$