Higher Order Differential Calculus on S L q (N)
Abstract
Let
Γ
be an
N
2
-dimensional bicovariant first order differential calculus on a Hopf algebra
S
L
q
(N)
. There are three possibilities to construct a differential Z-graded Hopf algebra
Γ
∧
which contains
Γ
as its first order part. Let
q
be a transcendental complex number. For
N>2
these three Z-graded Hopf algebras coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant
k
-forms. In this case each bi-invariant form is closed. In case of
4
D
±
calculi on
S
L
q
(2)
the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed.