Local index formulae on noncommutative orbifolds and equivariant zeta functions for the affine metaplectic group

We consider the algebra A of bounded operators on L2(Rn) generated by quantizations of isometric affine canonical transformations. The algebra A includes as subalgebras noncommutative tori of all dimensions and toric orbifolds. We define the spectral triple (A,H,D) with H=L2(Rn,Λ(Rn)) and the Euler operator D, a first order differential operator of index 1. We show that this spectral triple has simple dimension spectrum: For every operator B in the algebra Ψ(A,H,D) generated by the Shubin type pseudodifferential operators and the elements of A, the zeta function ζB(z)=Tr(B|D|−2z) has a meromorphic extension to C with at most simple poles. Our main result then is an explicit algebraic expression for the Connes-Moscovici cocycle. As a corollary we obtain local index formulae for noncommutative tori and toric orbifolds. © 2022 Elsevier Inc.

Авторы
Savin A. , Schrohe E.
Издательство
Academic Press Inc.
Язык
Английский
Статус
Опубликовано
Номер
108624
Том
409
Год
2022
Организации
  • 1 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 2 Leibniz University Hannover, Institute of Analysis, Welfengarten 1, Hannover, 30167, Germany
Ключевые слова
Local index formulae; Metaplectic operators; Noncommutative orbifolds; Spectral triple
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Vart P., Duivenvoorden R., Adema A., Covic A., Finne P., Braak N.H.-T., Laine K., Noordzij M., Schouten M., Jager K.J., Gansevoort R.T., Van der Net J.B., Essig M., Du Buf-Vereijken P.W.G., Van Ginneken B., Maas N., Van Jaarsveld B.C., Bemelman F.J., Klingenberg-Salahova F., Heenan-Vos F., Vervloet M.G., Nurmohamed A., Vogt L., Abramowicz D., Verhofstede S., Maoujoud O., Malfait T., Fialova J., Melilli E., Favà A., Cruzado J.M., Perez N.M., Lips J., Krepel H., Adilovic H., Radulescu D., Hengst M., Konings C., Rydzewski A., Braconnier P., Weis D., Gellert R., Oliveira J., Alferes D.G., Zakharova E.V., Ambühl P.M., Guidotti R., Walker A., Lepeytre F., Rabaté C., Rostoker G., Marques S., Azasevac T., Majstorovic G.S., Katicic D., Ten Dam M., Krüger T., Brzosko S., Liakopoulos V., Zanen A.L., Logtenberg S.J.J., Fricke L., Kuryata O., Slebe J.J.P., ElHafeez S.A., Kemlin D., Van de Wetering J., Reinders M.E.J., Hesselink D.A., Kal-van Gestel J., Eiselt J., Kielberger L., El-Wakil H.S., Verhoeven M., Logan I., Canal C., Facundo C., Ramos A.M., Debska-Slizien A., Veldhuizen N.M.H., Tigka E., Konsta M.A.P., Panagoutsos S., Mallamaci F., Postorino A., Cambareri F., Matceac I., Nistor I., Groeneveld J.H.M., Jousma J., Van Buren M., Diekmann F., Oppenheimer F., Blasco M., Pereira T.A., Santos A.C.S.Jr., Arias-Cabrales C., Crespo M., Llinàs-Mallol L., Buxeda A., Tàrrega C.B., Redondo-Pachon D., Jimenez M.D.A., Mendoza-Valderrey A., Martins A.C., Mateus C., Alvila G., Laranjinha I., Hofstra J.M., Siezenga M.A., Franco A., Arroyo D., Castellano S., Rodríguez-Ferrero M.L., Manzanos S.B., Barrios R.H.S., Lemahieu W., Bartelet K., Dirim A.B., Demir E., Sever M.S., Turkmen A., Şafak S., Hollander D.A.M.J., Büttner S., De Vries A.P.J., Meziyerh S., Van der Helm D., Mallat M., Bouwsma H., Sridharan S., Petruliene K., Maloney S.-R., Verberk I., Van der Sande F.M., Christiaans M.H.L., Hemmelder M.H., MohanKumar N., Di Luca M., Tuğlular S.Z., Kramer A.B., Beerenhout C., Luik P.T., Kerschbaum J., Tiefenthaler M., Watschinger B., Stepanov V.A., Zulkarnaev A.B., Turkmen K., Gandolfini I., Maggiore U., Fliedner A., Åsberg A., Mjoen G., Miyasato H., De Fijter C.W.H., Mongera N., Pini S., De Biase C., Kerckhoffs A., Van de Logt A.E., Maas R., Hilbrands L.B., Lebedeva O., Lopez V., Reichert L.J.M., Verhave J., Titov D., Parshina E.V., Zanoli L., Marcantoni C., Van Kempen G., Van Gils-Verrij L.E.A., Harty J.C., Meurs M., Myslak M., Battaglia Y., Lentini P., Den Deurwaarder E., Stendahl M., Rahimzadeh H., Rychlik I., Cabezas-Reina C.J., Roca A.M., Nauta F., Sahin İ., Goffin E., Kanaan N., Labriola L., Devresse A., Diaz-Mareque A., Coca A., De Arriba G., Meijers B.K.I., Naesens M., Kuypers D., Desschans B., Tonnerlier A., Wissing K.M., Dedinska I., Pessolano G., Malik S., Dounousi E., Papachristou E., Berger S.P., Sanders J.S.F., Franssen C.F.M., Özyilmaz A., Ponikvar J.B., Pernat A.M., Kovac D., Arnol M., Ekart R., Abrahams A.C., Molenaar F.M., Van Zuilen A.D., Meijvis S.C.A., Dolmans H., Tantisattamo E., Esposito P., Krzesinski J.-M., Barahira J.D., Gallieni M., Martin-Moreno P.L., Guglielmetti G., Guzzo G., Toapanta N., Soler M.J., Luik A.J., Van Kuijk W.H.M., Stikkelbroeck L.W.H., Hermans M.M.H., Rimsevicius L., Righetti M., Islam M.
Scientific Reports. Nature Publishing Group. Том 12. 2022.