{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T12:48:07Z","timestamp":1649162887878},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"S1","license":[{"start":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T00:00:00Z","timestamp":1566259200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Glasgow Math. J."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we define a Cayley\u2013Dickson process for <jats:italic>k<\/jats:italic>-coalgebras proving some results that describe the properties of the final coalgebra, knowing the properties of the initial one. Namely, after applying the Cayley\u2013Dickson process for <jats:italic>k<\/jats:italic>-coalgebras to a coassociative coalgebra, we obtain a coalternative one. Moreover, the first coalgebra is cocommutative if and only if the final coalgebra is coassociative. Finally we extend these results to a more general approach of <jats:italic>D<\/jats:italic>-coalgebras, where <jats:italic>D<\/jats:italic> is a <jats:italic>k<\/jats:italic>-coalgebra, presenting a class of examples of coalternative (non-coassociative) coalgebras obtained from group <jats:italic>D<\/jats:italic>-coalgebras.<\/jats:p>","DOI":"10.1017\/s0017089519000314","type":"journal-article","created":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T11:59:28Z","timestamp":1566302368000},"page":"S142-S164","source":"Crossref","is-referenced-by-count":1,"title":["COALTERNATIVE COALGEBRAS"],"prefix":"10.1017","volume":"62","author":[{"given":"HELENA","family":"ALBUQUERQUE","sequence":"first","affiliation":[]},{"given":"ELISABETE","family":"BARREIRO","sequence":"additional","affiliation":[]},{"given":"JOS\u00c9 M.","family":"S\u00c1NCHEZ","sequence":"additional","affiliation":[]},{"given":"CARLOS SONEIRA","family":"CALVO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,8,20]]},"reference":[{"key":"S0017089519000314_ref1","volume-title":"Hopf algebras","author":"Abe","year":"1980"},{"key":"S0017089519000314_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546495"},{"key":"S0017089519000314_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(01)00013-5"},{"key":"S0017089519000314_ref7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0783-2","volume-title":"Quantum groups","volume":"155","author":"Kassel","year":"1995"},{"key":"S0017089519000314_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700019316"},{"key":"S0017089519000314_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7850"},{"key":"S0017089519000314_ref8","volume-title":"Hopf algebras","author":"Sweedler","year":"1969"},{"key":"S0017089519000314_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2009.06.024"}],"container-title":["Glasgow Mathematical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0017089519000314","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,11]],"date-time":"2020-11-11T05:16:53Z","timestamp":1605071813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0017089519000314\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,20]]},"references-count":8,"journal-issue":{"issue":"S1","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["S0017089519000314"],"URL":"https:\/\/doi.org\/10.1017\/s0017089519000314","relation":{},"ISSN":["0017-0895","1469-509X"],"issn-type":[{"value":"0017-0895","type":"print"},{"value":"1469-509X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,20]]}}}