{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T22:42:45Z","timestamp":1759963365703},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,2,10]],"date-time":"2013-02-10T00:00:00Z","timestamp":1360454400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Math. Phys."],"published-print":{"date-parts":[[2013,3]]},"DOI":"10.1007\/s00220-013-1664-7","type":"journal-article","created":{"date-parts":[[2013,2,9]],"date-time":"2013-02-09T04:36:15Z","timestamp":1360384575000},"page":"675-716","source":"Crossref","is-referenced-by-count":8,"title":["A Supergeometric Approach to Poisson Reduction"],"prefix":"10.1007","volume":"318","author":[{"given":"A. S.","family":"Cattaneo","sequence":"first","affiliation":[]},{"given":"M.","family":"Zambon","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,2,10]]},"reference":[{"issue":"7","key":"1664_CR1","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1142\/S0217751X97001031","volume":"12","author":"M. Alexandrov","year":"1997","unstructured":"Alexandrov M., Schwarz A., Zaboronsky O., Kontsevich M.: The geometry of the master equation and topological quantum field theory. Internat. J. Mod. Phys. A 12(7), 1405\u20131429 (1997)","journal-title":"Internat. J. Mod. Phys. A"},{"key":"1664_CR2","unstructured":"Baez, J.C., Dolan, J.: Categorification. In: Higher category theory (Evanston, IL, 1997), Volume 230 of Contemp. Math. Providence, RI: Amer. Math. Soc., 1998, pp. 1\u201336"},{"key":"1664_CR3","unstructured":"Baez, J. C., Lauda, A.D.: Higher-dimensional algebra. V. 2-groups. Theory Appl. Categ. 12, 423\u2013491 (electronic) (2004)"},{"issue":"3","key":"1664_CR4","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0022-4049(92)90145-6","volume":"80","author":"R. Brown","year":"1992","unstructured":"Brown R., Mackenzie K.C.H.: Determination of a double Lie groupoid by its core diagram. J. Pure Appl. Algebra 80(3), 237\u2013272 (1992)","journal-title":"J. Pure Appl. Algebra"},{"key":"1664_CR5","unstructured":"Bursztyn, H., Cattaneo, A.S., Mehta, R., Zambon, M.: Generalized reduction via graded geometry. In preparation"},{"issue":"3","key":"1664_CR6","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s11005-004-4302-7","volume":"70","author":"I. Calvo","year":"2004","unstructured":"Calvo I., Falceto F.: Poisson reduction and branes in Poisson-sigma models. Lett. Math. Phys. 70(3), 231\u2013247 (2004)","journal-title":"Lett. Math. Phys."},{"key":"1664_CR7","doi-asserted-by":"crossref","first-page":"3721","DOI":"10.1090\/S0002-9947-09-04667-4","volume":"361","author":"A.S. Cattaneo","year":"2009","unstructured":"Cattaneo A.S., Zambon M.: Coisotropic embeddings in Poisson manifolds. Trans. A.M.S. 361, 3721\u20133746 (2009)","journal-title":"Trans. A.M.S."},{"key":"1664_CR8","unstructured":"Cattaneo, A.S., Zambon, M.: Graded geometry and Poisson reduction. American Institute of Physics Conference Proceedings 1093, College park, MD: Amer. Dist.of.Phys., 2009\u00a0pp. 48\u201356."},{"key":"1664_CR9","unstructured":"Coste, A., Dazord, P., Weinstein, A.: Groupo\u00ef des symplectiques. In Publications du D\u00e9partement de Math\u00e9matiques. Nouvelle S\u00e9rie. A, Vol. 2, Volume 87 of Publ. D\u00e9p. Math. Nouvelle S\u00e9r. A, Lyon: Univ. Claude-Bernard, 1987, pp. i\u2013ii, 1\u201362"},{"key":"1664_CR10","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s11005-008-0262-7","volume":"85","author":"F. Falceto","year":"2008","unstructured":"Falceto F., Zambon M.: An extension of the Marsden-Ratiu reduction for Poisson manifolds. Lett. Math. Phys. 85, 203\u2013219 (2008)","journal-title":"Lett. Math. Phys."},{"issue":"1\u20133","key":"1664_CR11","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s11005-009-0348-x","volume":"90","author":"R.L. Fernandes","year":"2009","unstructured":"Fernandes R.L., Iglesias Ponte D.: Integrability of Poisson-Lie group actions. Lett. Math. Phys. 90(1\u20133), 137\u2013159 (2009)","journal-title":"Lett. Math. Phys."},{"issue":"5","key":"1664_CR12","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1353\/ajm.0.0068","volume":"131","author":"R.L. Fernandes","year":"2009","unstructured":"Fernandes R.L., Ortega J.-P., Ratiu T.S.: The momentum map in Poisson geometry. Amer. J. Math. 131(5), 1261\u20131310 (2009)","journal-title":"Amer. J. Math."},{"key":"1664_CR13","unstructured":"Forrester-Barker, M.: Group objects and internal categories. http:\/\/arXiv.org\/abs\/math\/0212065vL [math.CT], 2002"},{"issue":"1","key":"1664_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1970528","volume":"84","author":"M. Gerstenhaber","year":"1966","unstructured":"Gerstenhaber M.: On the Deformation of Rings and Algebras: II. Ann. of Math. 84(1), 1\u201319 (1966)","journal-title":"Ann. of Math."},{"key":"1664_CR15","unstructured":"Khudaverdian, O.M.: Batalin-Vilkovisky formalism and odd symplectic geometry. In: Geometry and integrable models (Dubna, 1994), River Edge, NJ: World Sci. Publ., 1996, pp. 144\u2013181"},{"issue":"5","key":"1664_CR16","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.5802\/aif.1547","volume":"46","author":"Y. Kosmann-Schwarzbach","year":"1996","unstructured":"Kosmann-Schwarzbach Y.: From Poisson algebras to Gerstenhaber algebras. Ann. Inst. Fourier (Grenoble) 46(5), 1243\u20131274 (1996)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"key":"1664_CR17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s11005-004-0608-8","volume":"69","author":"Y. Kosmann-Schwarzbach","year":"2004","unstructured":"Kosmann-Schwarzbach Y.: Derived brackets. Lett. Math. Phys. 69, 61\u201387 (2004)","journal-title":"Lett. Math. Phys."},{"key":"1664_CR18","unstructured":"Lu, J.-H.: Multiplicative and affine poisson structures on lie groups, 1990, Ph.D. Thesis, U.C. Berkeley, available at http:\/\/hkumath.hku.hk\/~jhlu\/publications.html"},{"issue":"2","key":"1664_CR19","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0022-4049(89)90157-6","volume":"58","author":"K. Mackenzie","year":"1989","unstructured":"Mackenzie K.: Classification of principal bundles and Lie groupoids with prescribed gauge group bundle. J. Pure Appl. Algebra 58(2), 181\u2013208 (1989)","journal-title":"J. Pure Appl. Algebra"},{"key":"1664_CR20","doi-asserted-by":"crossref","unstructured":"Mackenzie, K.C.H.: General theory of Lie groupoids and Lie algebroids, Volume 213 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 2005","DOI":"10.1017\/CBO9781107325883"},{"issue":"2","key":"1664_CR21","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF00398428","volume":"11","author":"J.E. Marsden","year":"1986","unstructured":"Marsden J.E., Ratiu T.: Reduction of Poisson manifolds. Lett. Math. Phys. 11(2), 161\u2013169 (1986)","journal-title":"Lett. Math. Phys."},{"issue":"1","key":"1664_CR22","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.aim.2005.05.011","volume":"204","author":"I. Moerdijk","year":"2006","unstructured":"Moerdijk I., Mr\u010dun J.: On the integrability of Lie subalgebroids. Adv. Math. 204(1), 101\u2013115 (2006)","journal-title":"Adv. Math."},{"key":"1664_CR23","unstructured":"Roytenberg, D.: On the structure of graded symplectic supermanifolds and Courant algebroids. In: Quantization, Poisson brackets and beyond (Manchester, 2001), Volume 315 of Contemp. Math. Providence, RI: Amer. Math. Soc., 2002. pp. 169\u2013185"},{"issue":"2","key":"1664_CR24","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF02097392","volume":"155","author":"A. Schwarz","year":"1993","unstructured":"Schwarz A.: Geometry of Batalin-Vilkovisky quantization. Commun. Math. Phys. 155(2), 249\u2013260 (1993)","journal-title":"Commun. Math. Phys."},{"issue":"2","key":"1664_CR25","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02108080","volume":"158","author":"A. Schwarz","year":"1993","unstructured":"Schwarz A.: Semiclassical approximation in Batalin-Vilkovisky formalism. Commun. Math. Phys. 158(2), 373\u2013396 (1993)","journal-title":"Commun. Math. Phys."},{"key":"1664_CR26","unstructured":"\u0160evera, P.: Integration of Courant algebroids and its relatives (a first glance), Letter to Alan Weinstein. http:\/\/sophia.dtp.fmph.uniba.sk\/~severa\/letters\/no8.ps"},{"key":"1664_CR27","unstructured":"Va\u012dntrob, A.Y.: Lie algebroids and homological vector fields. Usp. Mat. Nauk, 52(2(314)), 161\u2013162 (1997). Translation in Russ. Math. Surve. 52, no. 2, 428\u2013429 (1997)"},{"key":"1664_CR28","doi-asserted-by":"crossref","unstructured":"Varadarajan, V.S.: Lie groups, Lie algebras, and their representations, Volume 102 of Graduate Texts in Mathematics. New York: Springer-Verlag 1984. reprint of the 1974 edition","DOI":"10.1007\/978-1-4612-1126-6"},{"key":"1664_CR29","doi-asserted-by":"crossref","unstructured":"Varadarajan, V.S.: Supersymmetry for mathematicians: an introduction, Volume 11 of Courant Lecture Notes in Mathematics. New York: New York University Courant Institute of Mathematical Sciences, 2004","DOI":"10.1090\/cln\/011"},{"key":"1664_CR30","doi-asserted-by":"crossref","unstructured":"Voronov, T.: Graded manifolds and Drinfeld doubles for Lie bialgebroids. In: Quantization, Poisson brackets and beyond (Manchester, 2001), Volume 315 of Contemp. Math., Providence, RI: Amer. Math. Soc., 2002, pp. 131\u2013168","DOI":"10.1090\/conm\/315"},{"key":"1664_CR31","unstructured":"Voronov, T.: Mackenzie theory and Q-manifolds. http:\/\/arxiv.org\/abs\/math\/0608111v2 [math.06], 2006"},{"key":"1664_CR32","unstructured":"Voronov, T.T.: Q-manifolds and higher analogs of Lie algebroids. In: XXIX Workshop on Geometric Methods in Physics, Volume 1307 of AIP Conf. Proc., Melville, NY: Amer. Inst. Phys, 2010, pp. 191\u2013202"},{"issue":"4","key":"1664_CR33","doi-asserted-by":"crossref","first-page":"705","DOI":"10.2969\/jmsj\/04040705","volume":"40","author":"A. Weinstein","year":"1988","unstructured":"Weinstein A.: Coisotropic calculus and Poisson groupoids. J. Math. Soc. Japan 40(4), 705\u2013727 (1988)","journal-title":"J. Math. Soc. Japan"},{"issue":"3","key":"1664_CR34","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1515\/form.2011.020","volume":"23","author":"C. Wockel","year":"2011","unstructured":"Wockel C.: Principal 2-bundles and their gauge 2-groups. Forum Math. 23(3), 565\u2013610 (2011)","journal-title":"Forum Math."},{"key":"1664_CR35","unstructured":"Zambon, M., Zhu, C.: Higher Lie algebra actions on Lie algebroids. J. Geom. Phys. 64, 155\u2013173 (2013). http:\/\/arxiv\/org\/abs\/1012.0428v2 [math.D6]"}],"container-title":["Communications in Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-013-1664-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00220-013-1664-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00220-013-1664-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T10:31:13Z","timestamp":1562668273000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00220-013-1664-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,10]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["1664"],"URL":"https:\/\/doi.org\/10.1007\/s00220-013-1664-7","relation":{},"ISSN":["0010-3616","1432-0916"],"issn-type":[{"value":"0010-3616","type":"print"},{"value":"1432-0916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,10]]}}}