The Relations of Inner and Outer Differential Calculi on Quantum Groups

Details The Relations of Inner and Outer Differential Calculi on Quantum Groups The Relations of Inner and Outer Differential Calculi on Quantum Groups

1998-08-21

arxiv.org/abs/math/9808095v2

Mathematics

Quantum Algebra

21 pages, LaTeX Revised version, with correction of several misprints and a slight reformulation

Scientific paper

The differential caluli $(Gamma,d)$ on quantum groups are classified due to the property of the generating element $X$ of its differential $d$. There are, on the one hand differential caluli which contain this element $X$ in the basis of one- forms that span $Gamma$, called Inner Differential Calculi. On the other hand, one has the differential caluli which do not contain the generating element $X$ of its differential $d$, thus they are called Outer Differential Calculi. We show that this two classes of differential caluli, for a given quantum group ${\cal A}$, are related by homomorphisms, which map the elements of one class on elements of the other class.

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