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Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras
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作者 yu xiu bai Leonid A.BOKUT +1 位作者 yu Qun CHEN Ze Rui ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第4期935-961,共27页
In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov ba... In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie algebras.We also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov basis theory for(unital)centroid hom-associative algebras.Finally,we prove that the"Poincaré-Birkhoff-Witt theorem"holds for certain type of centroid hom-Lie algebras over a field of characteristic 0,namely,every centroid hom-Lie algebra such that the eigenvectors of the mapβlinearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra,and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration. 展开更多
关键词 Centroid hom-Lie algebra centroid hom-associative algebra Gr?bner-Shirshov basis
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