Two Exterior Algebras for Orthogonal and Symplectic Quantum Groups

Let Γ be one of the N-dimensional bicovariant first order differential calculi on the quantum groups Oq(N) or Spq(N), where q is not a root of unity. We show that the second antisymmetrizer exterior algebra sΓ ∧ is the quotient of the universal exterior algebra uΓ ∧ by the principal ideal generated by θ∧θ. Here θ denotes the unique up to scalars bi-invariant 1-form. Moreover θ∧θ is central in uΓ ∧ and uΓ ∧ is an inner differential calculus. AMS subject classification: 58B30, 81R50