Representations of ?-conformai Galilei algebra and hierarchy of invariant equation

8th International Symposium on Quantum Theory and Symmetries

Aizawa, N.^1 ; Kimura, Y.^1 ; Segar, J.^2

Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Osaka 599-8531, Sakai, Japan^1

Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600 004, India^2

关键词: Central extensions;    Positive integer d;    Representation theory;    Semisimple Lie algebras;    Spin value;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012015/pdf
DOI  :  10.1088/1742-6596/512/1/012015

来源: IOP

【 摘 要 】

The -conformai Galilei algebra, denoted by g(d), is a particular non-semisimple Lie algebra specified by a positive integer d and a spin value . The algebra g(d) admits central extensions. We study lowest weight representations, in particular Verma modules, of g(d) with the central extensions for d = 1,2. We give a classification of irreducible modules over d 1 algebras and a condition of the Verma modules over d 2 algebras being reducible. As an application of the representation theory, hierarchies of differential equations are derived. The Lie group generated by g(d) with the central extension is a kinematical symmetry of the differential equations.