{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:09:11Z","timestamp":1773706151358,"version":"3.50.1"},"publisher-location":"Providence, Rhode Island","reference-count":8,"publisher":"American Mathematical Society","isbn-type":[{"value":"9781470441043","type":"print"},{"value":"9781470452377","type":"print"},{"value":"9781470452384","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"abstract":"<p>\n                    Panov proved necessary and sufficient conditions to extend the Hopf algebra structure of an algebra\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper R\">\n                        <mml:semantics>\n                          <mml:mi>R<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">R<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    to an Ore extension\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper R left-bracket x semicolon sigma comma delta right-bracket\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>R<\/mml:mi>\n                            <mml:mo stretchy=\"false\">[<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mi>\n                              \u03c3\n                              \n                            <\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>\n                              \u03b4\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">]<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">R[x;\\sigma ,\\delta ]<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"x\">\n                        <mml:semantics>\n                          <mml:mi>x<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">x<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    being a skew-primitive element. In this paper we extend Panov\u2019s result to Ore extensions over weak Hopf algebras. As an application we study Ore extensions of connected groupoid algebras.\n                  <\/p>","DOI":"10.1090\/conm\/727\/14641","type":"other","created":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T07:21:13Z","timestamp":1555053673000},"page":"277-292","source":"Crossref","is-referenced-by-count":1,"title":["Panov\u2019s theorem for weak Hopf algebras"],"prefix":"10.1090","author":[{"given":"Christian","family":"Lomp","sequence":"first","affiliation":[]},{"given":"Alveri","family":"Sant\u2019Ana","sequence":"additional","affiliation":[]},{"given":"Ricardo","family":"Leite dos Santos","sequence":"additional","affiliation":[]}],"member":"14","reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1006\/jabr.1999.7984","article-title":"Weak Hopf algebras. I. Integral theory and \ud835\udc36*-structure","volume":"221","author":"B\u00f6hm, Gabriella","year":"1999","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"2","isbn-type":"print","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1090\/conm\/585\/11614","article-title":"On the double crossed product of weak Hopf algebras","author":"B\u00f6hm, Gabriella","year":"2013","ISBN":"https:\/\/id.crossref.org\/isbn\/9780821875643"},{"key":"3","series-title":"Advanced Courses in Mathematics. CRM Barcelona","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8205-7","volume-title":"Lectures on algebraic quantum groups","author":"Brown, Ken A.","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/3764367148"},{"issue":"6","key":"4","doi-asserted-by":"publisher","first-page":"2405","DOI":"10.1016\/j.jpaa.2014.09.007","article-title":"Connected Hopf algebras and iterated Ore extensions","volume":"219","author":"Brown, K. A.","year":"2015","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"5","series-title":"London Mathematical Society Lecture Note Series","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546495","volume-title":"Corings and comodules","volume":"309","author":"Brzezinski, Tomasz","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0521539315"},{"issue":"1","key":"6","doi-asserted-by":"publisher","first-page":"31","DOI":"10.2969\/jmsj\/03310031","article-title":"Homological coalgebra","volume":"33","author":"Doi, Yukio","year":"1981","journal-title":"J. Math. Soc. Japan","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5645","issn-type":"print"},{"issue":"2","key":"7","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1006\/aima.2002.2081","article-title":"On the structure of weak Hopf algebras","volume":"170","author":"Nikshych, Dmitri","year":"2002","journal-title":"Adv. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-8708","issn-type":"print"},{"key":"8","isbn-type":"print","first-page":"211","article-title":"Finite quantum groupoids and their applications","author":"Nikshych, Dmitri","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/0521815126"}],"container-title":["Contemporary Mathematics","Rings, Modules and Codes"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T22:57:39Z","timestamp":1773701859000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/conm\/727\/14641\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9781470441043","9781470452377","9781470452384"],"references-count":8,"URL":"https:\/\/doi.org\/10.1090\/conm\/727\/14641","relation":{},"ISSN":["0271-4132","1098-3627"],"issn-type":[{"value":"0271-4132","type":"print"},{"value":"1098-3627","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]}}}