Classification of Bicovariant Differential Calculi on the Quantum Groups $SL_q(n+1)$ and $Sp_q(2n)$

I. Heckenberger; K. Schmuedgen

paper

Classification of Bicovariant Differential Calculi on the Quantum Groups $S L_{q} (n + 1)$ and $S p_{q} (2 n)$

arXiv:q-alg/9707032

Abstract

For transcendental values of $q$ all bicovariant first order differential calculi on the coordinate Hopf algebras of the quantum groups $S L_{q} (n + 1)$ and $S p_{q} (2 n)$ are classified. It is shown that the irreducible bicovariant first order calculi are determined by an irreducible corepresentation of the quantum group and a complex number $ζ$ such that $ζ^{n + 1} = 1$ for $S L_{q} (n + 1)$ and $ζ^{2} = 1$ for $S p_{q} (2 n)$ . Any bicovariant calculus is inner and its quantum Lie algebra is generated by a central element. The main technical ingredient is a result of the Hopf algebra $R (G_{q})^{0}$ for arbitrary simple Lie algebras.

21 pages, LaTeX2e, uses amstex.sty; extended version. To appear in J. reine angew. Math. (Crelle's Journal)

Classification of Bicovariant Differential Calculi on the Quantum Groups SLq​(n+1) and Spq​(2n)

Abstract

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Classification of Bicovariant Differential Calculi on the Quantum Groups $S L_{q} (n + 1)$ and $S p_{q} (2 n)$