Classification of low dimensional semi-associative 3-algebras

doi:10.3969/j.issn.1000-1565.2020.02.001

Journal of Hebei University (Natural Science Edition) ›› 2020, Vol. 40 ›› Issue (2): 113-118.DOI: 10.3969/j.issn.1000-1565.2020.02.001

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Classification of low dimensional semi-associative 3-algebras

BAI Ruipu,LIU Pei,ZHANG Yan

College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2019-05-20 Online:2020-03-25 Published:2020-03-25

Abstract

Abstract: The structure of semi-associative 3-algebras is studied.The classification of low dimensional semi-associative 3-algebras is given.It is proved that under isomorphism,there are only two classes of 3-dimensional semi-associative 3-algebras,four classes 4-dimensional semi-associative 3-algebras and six classes 5-dimensional semi-associative 3-algebras.And the concrete multiplications of each class of semi-associate 3-algebras in a basis are provided.

Key words: semi-associative 3-algebra, classification, 3-Lie algebra

CLC Number:

O152

BAI Ruipu,LIU Pei,ZHANG Yan. Classification of low dimensional semi-associative 3-algebras[J]. Journal of Hebei University (Natural Science Edition), 2020, 40(2): 113-118.

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Classification of low dimensional semi-associative 3-algebras

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