TY - JOUR

T1 - Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras

AU - Bai, Yu Xiu

AU - Bokut, Leonid A.

AU - Chen, Yu Qun

AU - Zhang, Ze Rui

N1 - Yuxiu Bai is supported by the grant of Guangzhou Civil Aviation College (Grant No. 22X0430); L.A. Bokut is supported by the RAS Fundamental Research Program (Grant No. FWNF-2022-0002), Yuqun Chen is supported by the NNSF of China (Grant Nos. 11571121, 12071156); Zerui Zhang is supported by the NNSF of China (Grant No. 12101248) and by the China Postdoctoral Science Foundation (Grant No. 2021M691099). Публикация для корректировки.

PY - 2024/4

Y1 - 2024/4

N2 - 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 Gröbner–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 map β linearly 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.

AB - 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 Gröbner–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 map β linearly 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.

KW - 13P10

KW - 17A01

KW - 17A30

KW - 17A50

KW - 17B35

KW - Centroid hom-Lie algebra

KW - Gröbner–Shirshov basis

KW - centroid hom-associative algebra

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85174170862&origin=inward&txGid=11f355839a4c8824f92dcf721c07fa43

UR - https://www.mendeley.com/catalogue/e9f9724f-d74c-3b71-b3b0-8ef497f26d5f/

U2 - 10.1007/s10114-023-2399-9

DO - 10.1007/s10114-023-2399-9

M3 - Article

VL - 40

SP - 935

EP - 961

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

SN - 1439-7617

IS - 4

ER -