Yang-Mills connections on quantum Heisenberg manifolds
DC Field | Value | Language |
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dc.contributor.author | Kang, S. | - |
dc.contributor.author | Luef, F. | - |
dc.contributor.author | Packer, J.A. | - |
dc.date.available | 2020-04-10T02:20:35Z | - |
dc.date.issued | 2020-03-01 | - |
dc.identifier.issn | 0022-247X | - |
dc.identifier.issn | 1096-0813 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/38163 | - |
dc.description.abstract | We investigate critical points and minimizers of the Yang-Mills functional YM on quantum Heisenberg manifolds Dμν c, where the Yang-Mills functional is defined on the set of all compatible linear connections on finitely generated projective modules over Dμν c. A compatible linear connection which is both a critical point and minimizer of YM is called a Yang-Mills connection. In this paper, we investigate Yang-Mills connections with constant curvature. We are interested in Yang-Mills connections on the following classes of modules over Dμν c: (i) Abadie's module Ξ of trace 2μ and its submodules; (ii) modules Ξ′ of trace 2ν; (iii) tensor product modules of the form PEμν c⊗Ξ, where Eμν c is Morita equivalent to Dμν c and P is a projection in Eμν c. We present a characterization of critical points and minimizers of YM, and provide a class of new Yang-Mills connections with constant curvature on Ξ over Dμν c via concrete examples. In particular, we show that every Yang-Mills connection ∇ on Ξ over Dμν c with constant curvature should have a certain form of the curvature such as [Formula presented]. Also we show that these Yang-Mills connections with constant curvature do not provide global minima but only local minima. We do this by constructing a set of compatible connections that are not critical points but their values are smaller than those of Yang-Mills connections with constant curvature. Our other results include: (i) an example of a compatible linear connection with constant curvature on Dμν c such that the corresponding connection on an isomorphic projective module does not have constant curvature, and (ii) the construction of a compatible linear connection with constant curvature which neither attains its minimum nor is a critical point of YM on Dμν c. Consequently the critical points and minimizers of YM depend crucially on the geometric structure of Dμν c and of the projective modules over Dμν c. Furthermore, we construct the Grassmannian connection on the projective modules Ξ′ with trace 2ν over Dμν c and compute its corresponding curvature. Finally, we construct tensor product connections on PEμν c⊗Ξ whose coupling constant is 2ν and characterize the critical points of YM for this projective module. © 2019 Elsevier Inc. | - |
dc.language | 영어 | - |
dc.language.iso | ENG | - |
dc.publisher | Academic Press Inc. | - |
dc.title | Yang-Mills connections on quantum Heisenberg manifolds | - |
dc.type | Article | - |
dc.identifier.doi | 10.1016/j.jmaa.2019.123604 | - |
dc.identifier.bibliographicCitation | Journal of Mathematical Analysis and Applications, v.483, no.1 | - |
dc.description.isOpenAccess | N | - |
dc.identifier.wosid | 000502181700020 | - |
dc.identifier.scopusid | 2-s2.0-85073744884 | - |
dc.citation.number | 1 | - |
dc.citation.title | Journal of Mathematical Analysis and Applications | - |
dc.citation.volume | 483 | - |
dc.type.docType | Article | - |
dc.publisher.location | 미국 | - |
dc.subject.keywordAuthor | Finitely generated projective modules | - |
dc.subject.keywordAuthor | Morita equivalence | - |
dc.subject.keywordAuthor | Quantum Heisenberg manifolds | - |
dc.subject.keywordAuthor | Tensor product connection | - |
dc.subject.keywordAuthor | Yang-Mills connections | - |
dc.subject.keywordPlus | MORITA EQUIVALENCE | - |
dc.subject.keywordPlus | REPRESENTATIONS | - |
dc.subject.keywordPlus | ALGEBRAS | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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