HIGHEST WEIGHT REPRESENTATIONS AND KAC DETERMINANTS FOR A CLASS OF CONFORMAL GALILEI ALGEBRAS WITH CENTRAL EXTENSION

DOI10.1142/S0129167X12501182zbMath1351.17007arXiv1204.2871MaRDI QIDQ4908358

Naruhiko Aizawa, Phillip S. Isaac, Yuta Kimura

Publication date: 5 March 2013

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2871

zbMATH Keywords

representationsVerma modulesKac determinantnon-semisimple Lie algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Lie algebras of Lie groups (22E60)

Related Items (15)

Structure of the planar Galilean conformal algebra ⋮ Dynamical realizations of $\mathcal {N}=1$N=1 l-conformal Galilei superalgebra ⋮ Irreducible representations of finite Lie conformal algebras of planar Galilean type ⋮ Whittaker modules and quasi-Whittaker modules for the Euclidean Lie algebra \(\mathfrak{e}(3)\) ⋮ The Lie algebra of the lowest transitively differential group of degree three ^* ⋮ Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules ⋮ A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras ⋮ On Casimir operators of conformal Galilei algebras ⋮ On simple modules over conformal Galilei algebras ⋮ NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE ⋮ Conformal Galilei algebras, symmetric polynomials and singular vectors ⋮ Higher-derivative mechanics with N=2l-conformal Galilei supersymmetry ⋮ Classification of finite dimensional uniserial representations of conformal Galilei algebras ⋮ Classification of simple weight modules over the 1-spatial ageing algebra ⋮ Generalized conformal pseudo-Galilean algebras and their Casimir operators

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