DOI 10.1007/s100520000470
Leibniz rules and reality conditions
G. Fiore1 - J. Madore2,3
1 Dip. di Matematica e Applicazioni, Fac. di Ingegneria,
Università di Napoli, V. Claudio 21, 80125 Napoli, Italy
2 Max-Planck-Institut für Physik
(Werner-Heisenberg-Institut),
Föhringer Ring 6, 80805 München, Germany
3 Laboratoire de Physique Théorique et Hautes Energies,
Université de Paris-Sud, Bâtiment 211, 91405 Orsay, France
Received: 6 June 2000 / Published online: 9 August 2000 - © Springer-Verlag 2000
Abstract
An analysis is made of reality conditions within the context
of non-commutative geometry. We show that if a covariant derivative
satisfies a given left Leibniz rule then a right Leibniz rule
fixes
the reality condition for the covariant derivative itself. We
show
also that the map which determines the right Leibniz rule must
satisfy
the braid equation if the extension of the covariant derivative
to
tensor products is to satisfy the reality condition.
Copyright Società Italiana di Fisica, Springer-Verlag 2000
