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.
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
.
DOI: 10.3969/j.issn.1000-1565.2020.02.001
[1] FILIPPOV V T.N-Lie algebras[J].Siberian Mathematical Journal,1986,26(6): 126-140.DOI:10.1007/bf00969110.
[2] 白瑞蒲,亢闯闯,马越,等.齐性Rota-Baxter 3-李代数(I)[J].河北大学学报(自然科学版),2018,38(1):1-6.DOI:10.3969/j.issn.1000-1565.2018.01.001.
[3] TAKHTAJAN L.On foundation of the genneralized Nambu mechanics[J].Communications in Mathematical Physics,1994,160: 295-315.DOI:10.1007/BF02103278.
[4] BAGGER J,LAMBERT N.Modeling multiple Mis[J].Physical Review,2007,D75: 045020.DOI:10.1103/PhyRevD.75.045020.
[5] BAGGER J,LAMBERT N.Gauge symmetry and supersymmetry of Multiple M2-branes[J].Physical Review,2008,D77: 065008.DOI:10.1103/PhyRevD.77.065008.
[6] HO P,HOU R,MATSUO Y.Lie 3-algebra and multiple M2-branes[J].High Energy Phys,2008,06:020.DOI:10.1088/1126-6708/2008/06/020.
[7] BAI R P,WU W Q,LI Z H.Some results on metric n-Lie algebras[J].Acta Mathematics Sinica,English Series,2012,28(6): 1209-1220.DOI:10.1007/s10114-011-0231-4.
[8] BAI R P,ZHANG Y.Semi-associative 3-algebras[J].arXiv: 1907.01706.arxiv.org/abs/1907.01726.
