Open this publication in new window or tab >>2019 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 136, p. 156-172Article in journal (Refereed) Published
Abstract [en]
We introduce Kahler-Poisson algebras as analogues of algebras of smooth functions on Kahler manifolds, and prove that they share several properties with their classical counterparts on an algebraic level. For instance, the module of inner derivations of a Kahler-Poisson algebra is a finitely generated projective module, and allows for a unique metric and torsion-free connection whose curvature enjoys all the classical symmetries. Moreover, starting from a large class of Poisson algebras, we show that every algebra has an associated Kahler-Poisson algebra constructed as a localization. At the end, detailed examples are provided in order to illustrate the novel concepts. (C) 2018 Elsevier B.V. All rights reserved.
Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2019
Keywords
Lie-Rinehart algebra; Kahler manifold; Levi-Civita connection; Curvature
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-154675 (URN)10.1016/j.geomphys.2018.11.001 (DOI)000456763300013 ()
Note
Funding Agencies|Swedish Research Council [621-2013-4538]
2019-03-012019-03-012020-01-20