Noncommutative Instantons on the 4-Sphere¶from Quantum Groups

Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2...
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Gespeichert in:

Autor*in:	Bonechi, F. [verfasserIn] Ciccoli, N. Tarlini, M.

Format:	Artikel
Sprache:	Englisch

Erschienen:	2002

Schlagwörter:	Vector Bundle Group Theory Quantum Group Unitary Representation Quantum Vector

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2002

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 226(2002), 2 vom: März, Seite 419-432
Übergeordnetes Werk:	volume:226 ; year:2002 ; number:2 ; month:03 ; pages:419-432

Links:	Volltext

DOI / URN:	10.1007/s002200200618

Katalog-ID:	OLC2038880077

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allfields	10.1007/s002200200618 doi (DE-627)OLC2038880077 (DE-He213)s002200200618-p DE-627 ger DE-627 rakwb eng 530 510 VZ Bonechi, F. verfasserin aut Noncommutative Instantons on the 4-Sphere¶from Quantum Groups 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2002 Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Vector Bundle Group Theory Quantum Group Unitary Representation Quantum Vector Ciccoli, N. aut Tarlini, M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 226(2002), 2 vom: März, Seite 419-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:226 year:2002 number:2 month:03 pages:419-432 https://doi.org/10.1007/s002200200618 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4125 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 226 2002 2 03 419-432
spelling	10.1007/s002200200618 doi (DE-627)OLC2038880077 (DE-He213)s002200200618-p DE-627 ger DE-627 rakwb eng 530 510 VZ Bonechi, F. verfasserin aut Noncommutative Instantons on the 4-Sphere¶from Quantum Groups 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2002 Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Vector Bundle Group Theory Quantum Group Unitary Representation Quantum Vector Ciccoli, N. aut Tarlini, M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 226(2002), 2 vom: März, Seite 419-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:226 year:2002 number:2 month:03 pages:419-432 https://doi.org/10.1007/s002200200618 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4125 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 226 2002 2 03 419-432
allfields_unstemmed	10.1007/s002200200618 doi (DE-627)OLC2038880077 (DE-He213)s002200200618-p DE-627 ger DE-627 rakwb eng 530 510 VZ Bonechi, F. verfasserin aut Noncommutative Instantons on the 4-Sphere¶from Quantum Groups 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2002 Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Vector Bundle Group Theory Quantum Group Unitary Representation Quantum Vector Ciccoli, N. aut Tarlini, M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 226(2002), 2 vom: März, Seite 419-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:226 year:2002 number:2 month:03 pages:419-432 https://doi.org/10.1007/s002200200618 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4125 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 226 2002 2 03 419-432
allfieldsGer	10.1007/s002200200618 doi (DE-627)OLC2038880077 (DE-He213)s002200200618-p DE-627 ger DE-627 rakwb eng 530 510 VZ Bonechi, F. verfasserin aut Noncommutative Instantons on the 4-Sphere¶from Quantum Groups 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2002 Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Vector Bundle Group Theory Quantum Group Unitary Representation Quantum Vector Ciccoli, N. aut Tarlini, M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 226(2002), 2 vom: März, Seite 419-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:226 year:2002 number:2 month:03 pages:419-432 https://doi.org/10.1007/s002200200618 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4125 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 226 2002 2 03 419-432
allfieldsSound	10.1007/s002200200618 doi (DE-627)OLC2038880077 (DE-He213)s002200200618-p DE-627 ger DE-627 rakwb eng 530 510 VZ Bonechi, F. verfasserin aut Noncommutative Instantons on the 4-Sphere¶from Quantum Groups 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2002 Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Vector Bundle Group Theory Quantum Group Unitary Representation Quantum Vector Ciccoli, N. aut Tarlini, M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 226(2002), 2 vom: März, Seite 419-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:226 year:2002 number:2 month:03 pages:419-432 https://doi.org/10.1007/s002200200618 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4125 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 226 2002 2 03 419-432
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title_full	Noncommutative Instantons on the 4-Sphere¶from Quantum Groups
author_sort	Bonechi, F.
journal	Communications in mathematical physics
journalStr	Communications in mathematical physics
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author_browse	Bonechi, F. Ciccoli, N. Tarlini, M.
container_volume	226
class	530 510 VZ
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author-letter	Bonechi, F.
doi_str_mv	10.1007/s002200200618
dewey-full	530 510
title_sort	noncommutative instantons on the 4-sphere¶from quantum groups
title_auth	Noncommutative Instantons on the 4-Sphere¶from Quantum Groups
abstract	Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. © Springer-Verlag Berlin Heidelberg 2002
abstractGer	Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. © Springer-Verlag Berlin Heidelberg 2002
abstract_unstemmed	Abstract: We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?7→?4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SUq(2); it determines a new deformation of the 4-sphere ∑4q as the algebra of coinvariants in ?q7. We show that the quantum vector bundle associated to the fundamental corepresentation of SUq(2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑4q, we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. © Springer-Verlag Berlin Heidelberg 2002
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container_issue	2
title_short	Noncommutative Instantons on the 4-Sphere¶from Quantum Groups
url	https://doi.org/10.1007/s002200200618
remote_bool	false
author2	Ciccoli, N. Tarlini, M.
author2Str	Ciccoli, N. Tarlini, M.
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doi_str	10.1007/s002200200618
up_date	2024-07-03T20:42:05.790Z
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