{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T21:25:36Z","timestamp":1745529936196},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p> Bol operators (Bols for short) are differential operators invariant under the projective action of [Formula: see text] between spaces of weighted densities on the 1-dimensional manifold. Here, we described analogs of Bols: [Formula: see text]-invariant differential operators between spaces of tensor fields on [Formula: see text]-dimensional supermanifolds with irreducible, as [Formula: see text]-modules, fibers of arbitrary, even infinite, dimension for certain \u201ckey\u201d values of [Formula: see text] and [Formula: see text] \u2014 the ones for which the solution is describable. We discovered many new operators for [Formula: see text] and for the case of [Formula: see text]-dimensional general superstring, which looks like a most natural superization of Bol\u2019s result, additional to the cases of super analogs of Bols between spaces of weighted densities on the [Formula: see text]-dimensional superstrings with a contact structure we classified in arXiv:2110.10504. In the case of fibers of dimension [Formula: see text], there are [Formula: see text]-parameter families of Bols, whereas there are no non-scalar nonzero differential operators between spaces of weighted densities. These two extreme answers justify the selection of cases here. <\/jats:p>","DOI":"10.1142\/s021819672250059x","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T07:40:30Z","timestamp":1659080430000},"page":"1345-1368","source":"Crossref","is-referenced-by-count":2,"title":["Analogs of Bol operators for \ud835\udd2d\ud835\udd24\ud835\udd29(a + 1|b) \u2282 \ud835\udd33\ud835\udd22\ud835\udd20\ud835\udd31(a|b)"],"prefix":"10.1142","volume":"32","author":[{"given":"Sofiane","family":"Bouarroudj","sequence":"first","affiliation":[{"name":"Division of Science and Mathematics, New York University Abu Dhabi, Po Box 129188, United Arab Emirates"}]},{"given":"Dimitry","family":"Leites","sequence":"additional","affiliation":[{"name":"Division of Science and Mathematics, New York University Abu Dhabi, Po Box 129188, United Arab Emirates"},{"name":"Department of Mathematics, Stockholm University, Stockholm, Sweden"}]},{"given":"Irina","family":"Shchepochkina","sequence":"additional","affiliation":[{"name":"Independent University of Moscow, B. Vlasievsky per., d. 11, RU-119 002 Moscow, Russia"}]}],"member":"219","published-online":{"date-parts":[[2022,8,27]]},"reference":[{"issue":"1","key":"S021819672250059XBIB001","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF01135536","volume":"11","author":"Bernstein J.","year":"1977","journal-title":"Funct. Anal. Appl."},{"issue":"2","key":"S021819672250059XBIB002","first-page":"143","volume":"1","author":"Bernstein J.","year":"1981","journal-title":"Sel. Math. Sov."},{"key":"S021819672250059XBIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF03343515"},{"issue":"4","key":"S021819672250059XBIB004","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1142\/S0218196722500345","volume":"32","author":"Bouarroudj S.","year":"2022","journal-title":"Int. J. Algebra Comput."},{"key":"S021819672250059XBIB005","unstructured":"P. Deligne,  P. Etingof,  D. Freed,  L. Jeffrey,  D. Kazhdan,  J. Morgan,  D. Morrison and  E. Witten (eds.),  Quantum Fields and Strings: A Course for Mathematicians, Vol.  1,  Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study,  Princeton, NJ, 1996\u20131997  (American Mathematical Society,  Providence, RI;  Institute for Advanced Study (IAS), Princeton, NJ, 1999),  xxii+723 pp."},{"key":"S021819672250059XBIB006","doi-asserted-by":"publisher","DOI":"10.1142\/9789812777065_0031"},{"key":"S021819672250059XBIB007","first-page":"217","volume-title":"General Topology and Applications","author":"Leites D.","year":"1991"},{"key":"S021819672250059XBIB008","doi-asserted-by":"publisher","DOI":"10.1070\/IM1974v008n04ABEH002129"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819672250059X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T07:59:13Z","timestamp":1669276753000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S021819672250059X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,27]]},"references-count":8,"journal-issue":{"issue":"07","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["10.1142\/S021819672250059X"],"URL":"https:\/\/doi.org\/10.1142\/s021819672250059x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,27]]}}}