Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles

Hannabuss, Keith C.; Mathai, Varghese

doi:10.1007/s11005-012-0574-5

Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles

Dec, 2010

15 pages

Published in:

Lett.Math.Phys. 102 (2012) 107-123

e-Print:

1012.2274 [math.QA]

DOI:

10.1007/s11005-012-0574-5

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Abstract: (arXiv)

In this paper, we initiate the study of nonassociative strict deformation quantization of C*-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as nonassociative strict deformation quantization of ordinary principal torus bundles. We then relate this to T-duality of principal torus bundles with

H

-flux. We also show that the Octonions fit nicely into our theory.

Note:

15 pages, latex2e, exposition improved, to appear in LMP

nonassociative strict deformation quantization
nonassociative torus
nonassociative torus bundles
T-duality
quantization: deformation
algebra: C*
fibre bundle: torus
differential forms: flux
T-duality
octonion

References(22)

Figures(0)

The Octonions

John C. Baez
(
- UC, Riverside, Math. Dept.
)

- Bull.Am.Math.Soc. 39 (2002) 145-205,
- Bull.Am.Math.Soc. 42 (2005) 213 (erratum)
•
e-Print:
- math/0105155
•
DOI:
- 10.1090/S0273-0979-01-00934-X

Twisted K theory and K theory of bundle gerbes

Peter Bouwknegt
(
- Adelaide U.
)
,
Alan L. Carey
(
- Adelaide U.
)
,
Varghese Mathai
(
- MIT, LNS and
- Adelaide U.
)
,
Michael K. Murray
(
- Adelaide U.
)
,
Danny Stevenson
(
- Adelaide U.
)

- Commun.Math.Phys. 228 (2002) 17-49
•
e-Print:
- hep-th/0106194
•
DOI:
- 10.1007/s002200200646

T duality: Topology change from H flux

- Commun.Math.Phys. 249 (2004) 383-415
•
e-Print:
- hep-th/0306062
•
DOI:
- 10.1007/s00220-004-1115-6

On the topology and H flux of T dual manifolds

- Phys.Rev.Lett. 92 (2004) 181601
•
e-Print:
- hep-th/0312052
•
DOI:
- 10.1103/PhysRevLett.92.181601

Nonassociative tori and applications to T-duality

- Commun.Math.Phys. 264 (2006) 41-69
•
e-Print:
- hep-th/0412092
•
DOI:
- 10.1007/s00220-005-1501-8

$C^{*}$ -Algebras in Tensor Categories

Peter Bouwknegt
(
- Australian Natl. U., Canberra
)
,
Keith C. Hannabuss
(
- Oxford U., Inst. Math. and
- Oxford U.
)
,
Varghese Mathai
(
- Adelaide U.
)

- Clay Math.Proc. 12 (2010) 127-166
•
e-Print:
- math/0702802

D-branes, B fields and twisted K theory

P. Bouwknegt
(
- Adelaide U.
)
,
V. Mathai
(
- Adelaide U.
)

- JHEP 03 (2000) 007
•
e-Print:
- hep-th/0002023
•
DOI:
- 10.1088/1126-6708/2000/03/007

Nonassociative star product deformations for D-brane world volumes in curved backgrounds

- Commun.Math.Phys. 225 (2002) 33-66
•
e-Print:
- hep-th/0101219
•
DOI:
- 10.1007/s002201000569

- Proc.Lond.Math.Soc. 99 1

Noncommutative principal torus bundles via parametrised strict deformation quantization

- Proc.Symp.Pure Math. 81 (2010) 133-148,
- AMS Proceedings of Symposia in Pure Mathematics 81 (2010) 133-148
•
e-Print:
- 0911.1886
•
DOI:
- 10.1090/pspum/081/2681761

Parametrised strict deformation quantization of C-bundles and Hilbert C-modules

Keith C. Hannabuss
(
- Oxford U., Inst. Math. and
- Balliol Coll., Oxford
)
,
Varghese Mathai
(
- Adelaide U.
)

- J.Austral.Math.Soc. 90 (2011) 25-38,
- J. Aust.Maths.Soc. 90 (2011) 25-38
•
e-Print:
- 1007.4696
•
DOI:
- 10.1017/S1446788711001170

Cyclicity of nonassociative products on D-branes

Manfred Herbst
(
- CERN
)
,
Alexander Kling
(
- Hannover U.
)
,
Maximilian Kreuzer
(
- Vienna, Tech. U.
)

- JHEP 03 (2004) 003
•
e-Print:
- hep-th/0312043
•
DOI:
- 10.1088/1126-6708/2004/03/003

- J.Funct.Anal. 257 1288

- Trans.Am.Math.Soc. 248 223

- Int.J.Math. 5 897

T duality for torus bundles with H fluxes via noncommutative topology

Varghese Mathai
(
- Adelaide U.
)
,
Jonathan M. Rosenberg
(
- Maryland U.
)

- Commun.Math.Phys. 253 (2004) 705-721
•
e-Print:
- hep-th/0401168
•
DOI:
- 10.1007/s00220-004-1159-7

On mysteriously missing T-duals, H-flux and the T-duality group

Varghese Mathai
(
- Adelaide U.
)
,
Jonathan M. Rosenberg
(
- Maryland U.
)

- pages 350-358, in Nankai Tracts Math., 10, World Sci. Publ., Hackensack, NJ, 2006,
- Differential Geometry and Physics: Proceedings. Edited by Mo-Lin Ge and Weiping Zhang, World Scientific, 2006. (Nankai Tracts in Mathematics). pp. 350-358
•
e-Print:
- hep-th/0409073
•
DOI:
- 10.1142/9789812772527_0030

T-duality for torus bundles with H-fluxes via noncommutative topology, II: The High-dimensional case and the T-duality group

Varghese Mathai
(
- Adelaide U. and
- Maryland U.
)
,
Jonathan M. Rosenberg
(
- Adelaide U. and
- Maryland U.
)

- Adv.Theor.Math.Phys. 10 (2006) 1, 123-158
•
e-Print:
- hep-th/0508084
•
DOI:
- 10.4310/ATMP.2006.v10.n1.a5

Nonassociative geometry: Towards discrete structure of space-time

Alexander I. Nesterov
(
- Guadalajara U. and
- Krasnoyarsk, Inst. Phys.
)
,
Lev V. Sabinin
(
- Quintana Roo U. and
- Moscow, Peoples Friendship U.
)

- Phys.Rev.D 62 (2000) 081501
•
e-Print:
- hep-th/0010159
•
DOI:
- 10.1103/PhysRevD.62.081501

- J.Nonlin.Mathematical Phys. 13 87

- Mem.Am.Math.Soc. 106 93

Mirror symmetry is T duality

Andrew Strominger
(
- UC, Santa Barbara
)
,
Shing-Tung Yau
(
- Harvard U.
)
,
Eric Zaslow
(
- Harvard U.
)

- Nucl.Phys.B 479 (1996) 243-259
•
e-Print:
- hep-th/9606040
•
DOI:
- 10.1016/0550-3213(96)00434-8