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Noncommutative Einstein manifolds
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Our modest aim is to give a reasonable generalization of this notion for the noncommutative setting along the lines sketched above: in noncommutative geometry the information about a space is basically encoded in a so–called spectral triple (A, H, D) consisting of an algebra A and an operator D, classically corresponding to the Dirac operator, both acting on a Hilbert space H2 and some further data and relations; a variation of the geometry corresponds to a certain variation of the spectral triple and a noncommutative Einstein space will be characterized as a2(D2), coming from the heat kernel asymptotics, being critical under particular variations.
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Noncommutative Einstein manifolds, Sven Schopka
- Sprache
- Erscheinungsdatum
- 2007
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- Titel
- Noncommutative Einstein manifolds
- Sprache
- Englisch
- Autor*innen
- Sven Schopka
- Verlag
- Shaker
- Erscheinungsdatum
- 2007
- Einband
- Paperback
- ISBN10
- 3832263098
- ISBN13
- 9783832263096
- Reihe
- Berichte aus der Mathematik
- Kategorie
- Skripten & Universitätslehrbücher
- Beschreibung
- Our modest aim is to give a reasonable generalization of this notion for the noncommutative setting along the lines sketched above: in noncommutative geometry the information about a space is basically encoded in a so–called spectral triple (A, H, D) consisting of an algebra A and an operator D, classically corresponding to the Dirac operator, both acting on a Hilbert space H2 and some further data and relations; a variation of the geometry corresponds to a certain variation of the spectral triple and a noncommutative Einstein space will be characterized as a2(D2), coming from the heat kernel asymptotics, being critical under particular variations.