Two Exterior Algebras for orthogonal and symplectic Quantum Groups

Details Two Exterior Algebras for orthogonal and symplectic Quantum Groups Two Exterior Algebras for orthogonal and symplectic Quantum Groups

1999-06-08

arxiv.org/abs/math/9906044v1

Mathematics

Quantum Algebra

20 pages, 10 figures, uses bbm, amsmath, mathrsfs

Scientific paper

Let \Gamma be 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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