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Dirac cohomology and translation functors


Mehdi, Salah; Pandžić, Pavle
Dirac cohomology and translation functors // Journal of algebra, 375 (2013), 328-336 doi:10.1016/j.jalgebra.2012.11.022 (međunarodna recenzija, članak, znanstveni)


Naslov
Dirac cohomology and translation functors

Autori
Mehdi, Salah ; Pandžić, Pavle

Izvornik
Journal of algebra (0021-8693) 375 (2013); 328-336

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
(g; K)-module; Dirac operator; Dirac cohomology; translation functor.

Sažetak
We study the relationship between the Dirac cohomology of a $(\fg, K)$-module $X$ and the Dirac cohomology of a Jantzen-Zuckerman translate of $X$. More precisely, we show that if $X$ is unitary, and if some submodule $X'$ of a translate of $X$ has nonzero Dirac cohomology, then $X$ has nonzero Dirac cohomology. In the course of the proof, we show that the space of harmonic spinors (i.e., the kernel of the Dirac operator) related to $X'$ embeds into a sort of product of harmonic spinors for $X$ and harmonic spinors for the finite-dimensional module used to define the translation. This generalizes results of \cite{; ; ; MP08}; ; ; and \cite{; ; ; MP09}; ; ; .

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
037-0372794-2807 - Homološke i geometrijske metode u teoriji reprezentacija (Pavle Pandžić, )
037-0372794-3229 - Reprezentacije poluprostih Liejevih grupa: K-tipovi, duali, C*-algebre (Hrvoje Kraljević, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Pavle Pandžić, (135772)

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka:


  • MathSciNet
  • Zentrallblatt für Mathematik/Mathematical Abstracts


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