대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제48권3호
  • /
  • Pages.505-521
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  • 2011
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A REMARK ON GEL'FAND DUALITY FOR SPECTRAL TRIPLES

  • Bertozzini, Paolo (Department of Mathematics and Statistics Faculty of Science and Technology Thammsat University - Rangsit Campus) ;
  • Conti, Roberto (Mathematics School of Mathematical and Physical Sciences University of Newcastle) ;
  • Lewkeeratiyutkul, Wicharn (Department of Mathematics Faculty of Science Chulalongkorn University)
  • 투고 : 2009.09.10
  • 발행 : 2011.05.31
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초록

We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-$C^*$-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in [5] into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.

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참고문헌

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