000161882 001__ 161882
000161882 005__ 20251017144622.0
000161882 0247_ $$2doi$$a10.4171/DM/1006
000161882 0248_ $$2sideral$$a144519
000161882 037__ $$aART-2025-144519
000161882 041__ $$aeng
000161882 100__ $$0(orcid)0000-0002-6497-2162$$aElduque, Alberto$$uUniversidad de Zaragoza
000161882 245__ $$aAlmost fine gradings on algebras and classification of gradings up to isomorphism
000161882 260__ $$c2025
000161882 5060_ $$aAccess copy available to the general public$$fUnrestricted
000161882 5203_ $$aWe consider the problem of classifying gradings by groups on a finite-dimensional algebra A (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such that every G-grading on A is obtained from an almost fine grading on A in an essentially unique way, which is not the case with fine gradings. For abelian G, we give a method of obtaining all almost fine gradings if fine gradings are known. We apply these ideas to the case of semisimple Lie algebras in characteristic 0: to any abelian group grading with nonzero identity component, we attach a (possibly nonreduced) root system Φ and, in the simple case, construct an adapted Φ-grading.
000161882 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-23R$$9info:eu-repo/grantAgreement/EUR/ISCII-ERDF/A way to make Europe$$9info:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21
000161882 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000161882 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000161882 700__ $$aKochetov, Mikhail
000161882 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra
000161882 773__ $$g30, 4 (2025), 887-908$$pDoc. math.$$tDocumenta Mathematica$$x1431-0635
000161882 8564_ $$s340242$$uhttps://zaguan.unizar.es/record/161882/files/texto_completo.pdf$$yVersión publicada
000161882 8564_ $$s1593634$$uhttps://zaguan.unizar.es/record/161882/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000161882 909CO $$ooai:zaguan.unizar.es:161882$$particulos$$pdriver
000161882 951__ $$a2025-10-17-14:22:10
000161882 980__ $$aARTICLE