Boson realizations of the semi-simple Lie algebras

Miloslav Havlicek (dekan@fjfi.cvut.cz)
Department of Mathematics
Faculty of Nuclear Sciences and Physical Engineering
Czech Technical University of Prague
Trojanova 13, 120 00 Prague 2
Czech Republic

Abstract

A short review of the construction of the boson realizations of the semi-simple Lie algebras is given. The method is illustrated on examples. An application for the construction of matrix differential realizations is mentioned and their properties are studied. It is shown how alternatively the concept of a Lie field can be used.