Morita theory in deformation quantization |
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Authors: | Stefan Waldmann |
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Institution: | (1) Départment de Mathématiques, Université Libre de Bruxelles, CP 218, Campus Plaine, 1050 Brussels, Belgium;(2) Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann Herder Straß e 3, D 79104 Freiburg, Germany |
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Abstract: | Various aspects of Morita theory of deformed algebras and in particular of star product algebras on general Poisson manifolds
are discussed. We relate the three flavours ring-theoretic Morita equivalence, *-Morita equivalence, and strong Morita equivalence
and exemplify their properties for star product algebras. The complete classification of Morita equivalent star products on
general Poisson manifolds is discussed as well as the complete classification of covariantly Morita equivalent star products
on a symplectic manifold with respect to some Lie algebra action preserving a connection. |
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