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arXiv math/99060441999-06-08math.QA

正交辛量子群的两个外代数

Two Exterior Algebras for orthogonal and symplectic Quantum Groups

Axel Schueler

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

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摘要：

设Γ是正交或辛量子群O_q（N）或Sp_q（N）上的N^2维双共变一阶微分演算.参数q不是单位单位根。我们证明了第二反对称化子外代数是泛外代数U与w^2生成的主理想的商。这里w表示唯一的直到标量的双不变1-形式。此外，w^2是U的中心，U是一个内微分学。

英文摘要：

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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