Introduction to Superalgebra

Abstract

This chapter contains preparatory information for the following ones. Here we lay out the principal facts about supermanifolds, spaces on which some of the coordinate functions commute and the others anti-commute. Recently it has become clear that the whole apparatus of commutative algebra, of the theory of Lie groups, of algebraic, analytic and differential geometry permits the systematic introduction of anti-commuting (odd, fermion) quantities. This process significantly enriches these structures and results in extremely non-trivial variants of them in “supermathematics.”