Invariant integration on classical and quantum Lie supergroups

Abstract

Invariant integrals on Hopf superalgebras, in particular, the classical and quantum Lie supergroups, are studied. The uniqueness ~up to scalar multiples! of a left integral is proved, and a Z2-graded version of Maschke’s theorem is discussed. A construction of left integrals is developed for classical and quantum Lie supergroups. Applied to several classes of examples the construction yields the left integrals in explicit form.