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Two Exterior Algebras for orthogonal and symplectic Quantum Groups

Axel Schueler
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Abstract

Let Γbe one of the N^2-dimensional bicovariant first order differential calculi on the orthogonal or symplectic quantum group O_q(N) or Sp_q(N). The parameter q is not a root of unity. We show that the second antisymmetrizer exterior algebra is the quotient of the universal exterior algebra U by the principal ideal generated by w^2. Here w denotes the unique up to scalars bi-invariant 1-form. Moreover w^2 is central in U and U is an inner differential calculus.

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Axel Schueler. 1999-06-08. Two Exterior Algebras for orthogonal and symplectic Quantum Groups. https://arxiv.org/abs/math/9906044

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