{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:02:33Z","timestamp":1756425753701,"version":"3.44.0"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algebra Colloq."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> In the current work, we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras, and hence of split Lie algebras. In particular, we show that an arbitrary graded regular BiHom-Lie algebra [Formula: see text] can be expressed as [Formula: see text], where [Formula: see text] is a linear subspace in [Formula: see text], 1 being the neutral element of the grading group, and any [Formula: see text] a well-described (graded) ideal of [Formula: see text], satisfying [Formula: see text] if [Formula: see text]. Moreover, under some conditions, we characterize the simplicity of [Formula: see text] and we show that [Formula: see text] is the direct sum of the family of its simple (graded) ideals. <\/jats:p>","DOI":"10.1142\/s1005386725000318","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T06:41:35Z","timestamp":1756363295000},"page":"429-442","source":"Crossref","is-referenced-by-count":0,"title":["Graded Regular BiHom-Lie Algebras"],"prefix":"10.1142","volume":"32","author":[{"given":"Elisabete","family":"Barreiro","sequence":"first","affiliation":[{"name":"University of Coimbra, CMUC, Department of Mathematics, FCTUC, Largo D. Dinis 3000-143 Coimbra, Portugal"}]},{"given":"A.J.","family":"Calder\u00f3n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de C\u00e1diz, Puerto Real, Spain"}]},{"given":"Rosa M.","family":"Navarro","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, C\u00e1ceres, Spain"}]},{"given":"Jos\u00e9 M.","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de C\u00e1diz, Puerto Real, Spain"}]}],"member":"219","published-online":{"date-parts":[[2025,8,29]]},"container-title":["Algebra Colloquium"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1005386725000318","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T06:41:37Z","timestamp":1756363297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1005386725000318"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,29]]},"references-count":0,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S1005386725000318"],"URL":"https:\/\/doi.org\/10.1142\/s1005386725000318","relation":{},"ISSN":["1005-3867","0219-1733"],"issn-type":[{"value":"1005-3867","type":"print"},{"value":"0219-1733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,29]]}}}