Extensions and degeneration of spectral triples

Erik Christensen; Cristina Ivan

doi:10.1007/s00220-008-0657-4

Extensions and degeneration of spectral triples

Erik Christensen, Cristina Ivan

Institut for Matematiske Fag

3 Citationer (Scopus)

Abstract

Til et ikke kommutativt kompakt metrisk rum, som er tilknyttet en C*-algebra A og en extension E af A, konstrueres en 2-parameter familie af kompakte ikke kommutative metriske rum tilknyttet E. Det vises, at under visse grænseovergange i parameterrummet vil de tilknyttede metriske rum konvergere i kvante Gromov-Hausdorff metrikken mod enten det oprindeligt givne ikke kommutative rum, knyttet til A, eller mod et ikke kommutativt rum, der er tilknyttet de kompakte operatorer.

Originalsprog	Engelsk
Tidsskrift	Communications in Mathematical Physics
Vol/bind	285
Udgave nummer	3
Sider (fra-til)	925-955
Antal sider	31
ISSN	0010-3616
DOI	https://doi.org/10.1007/s00220-008-0657-4
Status	Udgivet - 2009

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10.1007/s00220-008-0657-4

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title = "Extensions and degeneration of spectral triples",

abstract = "To a compact non commutative metric space associated to a C*-algebra A and an extension E of A, we construct 2-parameter family of compact non commutative metric spaces associated to E. It is shown that under certain limits along paths in the parameter space the corresponding spaces converge in the quantum Gromov-Hausdorff metric towards either the given non commutative metric space or towards a compact non commutative metric space associated to the compact operators.",

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year = "2009",

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language = "English",

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T1 - Extensions and degeneration of spectral triples

AU - Christensen, Erik

AU - Ivan, Cristina

PY - 2009

Y1 - 2009

N2 - To a compact non commutative metric space associated to a C*-algebra A and an extension E of A, we construct 2-parameter family of compact non commutative metric spaces associated to E. It is shown that under certain limits along paths in the parameter space the corresponding spaces converge in the quantum Gromov-Hausdorff metric towards either the given non commutative metric space or towards a compact non commutative metric space associated to the compact operators.

AB - To a compact non commutative metric space associated to a C*-algebra A and an extension E of A, we construct 2-parameter family of compact non commutative metric spaces associated to E. It is shown that under certain limits along paths in the parameter space the corresponding spaces converge in the quantum Gromov-Hausdorff metric towards either the given non commutative metric space or towards a compact non commutative metric space associated to the compact operators.

U2 - 10.1007/s00220-008-0657-4

DO - 10.1007/s00220-008-0657-4

M3 - Journal article

SN - 0010-3616

VL - 285

SP - 925

EP - 955

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Extensions and degeneration of spectral triples

Abstract

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