Open AccessThe method of virtual copies and contractions of simple Lie algebras
Author(s) -
Rutwig Campoamor-Stursberg
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1612/1/012006
Subject(s) - lie algebra , simple (philosophy) , subalgebra , context (archaeology) , algorithm , mathematics , algebra over a field , pure mathematics , philosophy , geology , epistemology , paleontology
Contractions of simple Lie algebras onto semidirect sums are analyzed in the context of the method of virtual copies, and various existence conditions are obtained in terms of the branching rules of representations and the properties of the characteristic representation associated to an embedding of semisimple algebras. Contractions of the Lie algebra s p ( 2 N , ℝ ) with respect to nonmaximal symplectic subalgebras are studied in some detail. In particular, a realization of the subalgebra in terms of cubic polynomial operators is constructed.