{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T18:05:47Z","timestamp":1758477947930},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"Simons Foundation collaboration","award":["712462"],"award-info":[{"award-number":["712462"]}]},{"name":"the Estonian Research Council through the Mobilitas Pluss scheme","award":["MOBJD679"],"award-info":[{"award-number":["MOBJD679"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions. <\/jats:p>","DOI":"10.1142\/s0218196722500424","type":"journal-article","created":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T05:48:22Z","timestamp":1652939302000},"page":"985-1007","source":"Crossref","is-referenced-by-count":4,"title":["Derivation problem for quandle algebras"],"prefix":"10.1142","volume":"32","author":[{"given":"M.","family":"Elhamdadi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of South Florida, Tampa, FL 33620, USA"}]},{"given":"A.","family":"Makhlouf","sequence":"additional","affiliation":[{"name":"IRIMAS - d\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Haute Alsace, 18 rue des Fr\u00e8res Lumi\u00e8re, 68093 Mulhouse, France"}]},{"given":"S.","family":"Silvestrov","sequence":"additional","affiliation":[{"name":"Division of Mathematics and Physics, School of Education, Culture and Communication, M\u00e4lardalen University, Box 883, 72123 V\u00e4ster\u00e5s, Sweden"}]},{"given":"E.","family":"Zappala","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Statistics, University of Tartu, Narva mnt 18, 51009 Tartu, Estonia"}]}],"member":"219","published-online":{"date-parts":[[2022,5,18]]},"reference":[{"key":"S0218196722500424BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498819501573"},{"key":"S0218196722500424BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2019.02.011"},{"key":"S0218196722500424BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/stml\/074"},{"key":"S0218196722500424BIB005","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611500012338"},{"key":"S0218196722500424BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(82)90077-9"},{"key":"S0218196722500424BIB007","doi-asserted-by":"publisher","DOI":"10.2307\/1970433"},{"key":"S0218196722500424BIB008","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2008.168.221"},{"issue":"161","key":"S0218196722500424BIB009","first-page":"160","volume":"119","author":"Matveev S. V.","year":"1982","journal-title":"Mat. Sb. (N.S.)"},{"key":"S0218196722500424BIB011","volume-title":"The algebraic structure of group rings","author":"Passman D. S.","year":"1985"},{"key":"S0218196722500424BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1949-09281-9"},{"key":"S0218196722500424BIB013","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1955-09974-9"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196722500424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T08:35:06Z","timestamp":1655886906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196722500424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,18]]},"references-count":11,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1142\/S0218196722500424"],"URL":"https:\/\/doi.org\/10.1142\/s0218196722500424","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,18]]}}}