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Two Exterior Algebras for Orthogonal and Symplectic Quantum Groups

Published online by Cambridge University Press:  04 December 2007

Axel Schüler
Axel Schüler
Affiliation:
Department of Mathematics, University of Leipzig, Augustusplatz 10, 04109 Leipzig, Germany. E-mail: [email protected]
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Abstract

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Let Γ be one of the N2-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 ∧ denotes the unique up to scalars bi-invariant 1-form. Moreover, θ∧θ is central in uΓ∧ and uΓ∧ is an inner differential calculus.

Keywords

bicovariant differential calculusexterior algebraquantum group
Type
Research Article
Information
Compositio Mathematica , Volume 126 , Issue 1 , March 2001 , pp. 57 - 77
Copyright
© 2001 Kluwer Academic Publishers