Review on Root System of Lie Superalgebras and Some Partial Results on Splints of A(m,n)

Abstract

Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. This dissertation deals with the splints of the root systems of Classical Lie superalgebra which can be seen as a generalisation of a Lie algebra to include a Z2 − grading. The term ’Splints’ is first coined by David A Richter which play an important role in determining the branching rules of a module over a complex semisimple Lie algebra. These results have been extended to classical Lie superalgebras which gave interesting results with regards to the graded algebras.