Commutator Representations of Covariant Differential Calculi on Quantum Groups |
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Authors: | Schmüdgen Konrad |
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Institution: | (1) Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany |
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Abstract: | Let (, d) be a first-order differential *-calculus on a *-algebra
. We say that a pair (, F) of a *-representation of
on a dense domain
of a Hilbert space and a symmetric operator F on
gives a commutator representation of if there exists a linear mapping : L(
) such that (adb) = (a)iF, (b) ], a, b
. Among others, it is shown that each left-covariant *-calculus of a compact quantum group Hopf *-algebra
has a faithful commutator representation. For a class of bicovariant *-calculi on
, there is a commutator representation such that F is the image of a central element of the quantum tangent space. If
is the Hopf *-algebra of the compact form of one of the quantum groups SL
q
(n+1), O
q
(n), Sp
q
(2n) with real trancendental q, then this commutator representation is faithful. |
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Keywords: | quantum groups noncommutative geometry |
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