A DOLBEAULT-DIRAC SPECTRAL TRIPLE FOR QUANTUM PROJECTIVE SPACE
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420730" target="_blank" >RIV/00216208:11320/20:10420730 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=B8ZM4XnQOD" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=B8ZM4XnQOD</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.25537/dm.2020v25.1079-1157" target="_blank" >10.25537/dm.2020v25.1079-1157</a>
Alternative languages
Result language
angličtina
Original language name
A DOLBEAULT-DIRAC SPECTRAL TRIPLE FOR QUANTUM PROJECTIVE SPACE
Original language description
The notion of a Kahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of quantum flag manifolds. It was subsequently shown that any covariant positive definite Kahler structure has a canonically associated triple satisfying, up to the compact resolvent condition, Connes' axioms for a spectral triple. In this paper we begin the development of a robust framework in which to investigate the compact resolvent condition, and moreover, the general spectral behaviour of covariant Kahler structures. This framework is then applied to quantum projective space endowed with its Heckenberger-Kolb differential calculus. An even spectral triple with non-trivial associated K-homology class is produced, directly q-deforming the Dolbeault-Dirac operator of complex projective space. Finally, the extension of this approach to a certain canonical class of irreducible quantum flag manifolds is discussed in detail.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Documenta Mathematica
ISSN
1431-0643
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
25
Country of publishing house
DE - GERMANY
Number of pages
79
Pages from-to
1079-1157
UT code for WoS article
000592702600034
EID of the result in the Scopus database
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