COMPUTING THE INVARIANTS OF LIE SUPER-ALGEBRAS

Lie superalgebras (LS) generalise the class of Lie algebras (LA) by admitting a bracket multiplication which is sometimes commutative and sometimes anticommutative. It is known that such algebras can be represented by first-order Grassmann differential operators acting on Euclidean superfields. This leads, by generalising the usual procedure for LA, to a method for computing the Casimir invariants of any LS: first solve a system of Grassmann differential equations to obtain the invariants of the graded symmetric algebra, and then map onto the centre of the enveloping algebra by means of the graded symmetrising isomorphism.