True BRST symmetry algebra and the theory of its representations

A simple treatment of BRST symmetry is proposed. From the physical point of view, it expresses a symmetry between ghosts and spurions; from the mathematical point of view, the symmetry operations are linear transformations in the superspaee $C_{1,1}$. From this it follows that the true BRST symmetry algebra is $l(1,1)$, the Lie superalgebra of all linear endomorphisms of $C_{1,1}$, which extends the usual BRST algebra of the generators $Q$ and $Q_c$ with two new generators $K=Q^*$ and $R=\{Q,Q^*\}$. The theory of the representations of $l(1,1)$ is developed systematically. The sets of automorphisms and involutions of $l(1,1)$ are described. Decompositions into irreducible and indecomposable components are constructed for large classes of representations, both finiteand infinite-dimensional. Particular attention is devoted to the analysis of the indecomposable representations (in particular, a connection between them and subspaces of the continuous spectrum of the generators is found) and also of the metric properties of the indefinite spaces of the representations. A class of physical representations is identified and described in detail.