齐次Rota-Baxter 3-李代数(Ⅰ)
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摘要
无限维单3-李代数Aω=∑m∈ZFLm上的齐性Rota-Baxter算子R是Aω的Rota-Baxter算子,且满足R(Lm)=f(m)Lm,其中f:Z→F.因为当λ不等于0时,3-李代数的权为λ的Rota-Baxter算子完全由权为1的Rota-Baxter算子所决定.因此,本文主要研究了Aω上权为1且满足|W1|<∞的齐性RotaBaxter算子的结构,并在3-李代数Aω的基底空间A上利用齐次Rota-Baxter算子构造了5类3-代数(A,[,,]j),并证明了3-李代数(A,[,,]j)都是齐性Rota-Baxter 3-李代数.
Homogeneous Rota-Baxter operators R on the infinite dimensional simple 3-Lie Algebra Aω=∑m∈ZFLm,are Rota-Baxter operators which satisfy R(L_m) = f(m)L_m, where f : Z→Fis a function.Since Rota-Baxter operators of weight λ with λ≠0 on 3-Lie algebras are completely determined by the caseλ=1, the homogeneous Rota-Baxter operators of weight 1 on A_ω with | W_1 | <∞ are discussed. Five 3-Lie algebras(A,[,,]_j) are constructed by the simple 3-Lie algebra A_ω and its homogeneous Rota-Baxter operators. And it is proved that 3-Lie algebras(A,[,,]_j) are all homogeneous Rota-Baxter 3-Lie algebras.
Homogeneous Rota-Baxter operators R on the infinite dimensional simple 3-Lie Algebra Aω=∑m∈ZFLm,are Rota-Baxter operators which satisfy R(L_m) = f(m)L_m, where f : Z→Fis a function.Since Rota-Baxter operators of weight λ with λ≠0 on 3-Lie algebras are completely determined by the caseλ=1, the homogeneous Rota-Baxter operators of weight 1 on A_ω with | W_1 | <∞ are discussed. Five 3-Lie algebras(A,[,,]_j) are constructed by the simple 3-Lie algebra A_ω and its homogeneous Rota-Baxter operators. And it is proved that 3-Lie algebras(A,[,,]_j) are all homogeneous Rota-Baxter 3-Lie algebras.
引文
[1]BAXTER G.An analytic problem whose solution follows from a simple algebraic identity[J].Pacific J Math,1960,10:731-742.DOI:10.2140/pjm.1960.10.731.
[2]BAI C,BELLIER O,GUO L,et al.Spliting of operations,Manin products and Rota-Baxter operators[J].IMRN,2012,10:193-266.DOI:10.1093/imrn/rnr266.
[3]CARTIER P.On the structure of free Baxter algebras[J].Adv Math,1972,9:253-265.DOI:10.1016/0001-8708(72)90018-7.
[4]EBRAHIMI-FARD K,GUO L,KREIMER D.Spitzer's identity and the algebraic Birkhoff decomposition in pQFT[J].J Phys A:Math Gen,2004,37:11037-11052.DOI:10.1088/0305-4470/37/45/020.
[5]EBRAHIMI-FARD K,GUO L,MANCHON D.Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion[J].Comm Math Phys,2006,267:821-845.DOI:10.1007/s00220-00b-0080-7.
[6]BAI R,GUO L,LI Q,WU Y.Rota-Baxter 3-Lie algebras[J].J Math Phys,2013,54(6):3504.DOI:10.1063/1.4808053.
[7]BAI C,GUO L,SHENG Y.Bialgebras,the classical Yang-Baxter equation and manin triples for 3-Lie algebras[J/OL].[2017-01-03],https:/arxiv.org/:1604.0599v1[math-ph].
[8]BAI R,ZHANG Y.Homogeneous Rota-Baxter operators on 3-Lie algebra Aω[J/OL].Colloq Math,[2017-01-06],https://arxiv.org/abs/1512.02261/.DOI:10.4064/cm6829-2-2016.
[9]BAI R,ZHANG Y.Homogeneous Rota-Baxter operators on 3-Lie algebra Aω(II)[J/OL].Matp-ph.[2017-01-06],https://arxiv.org/abs/.1615.02252v2.DOI:10.4064/cm7000-4-2017.
[10]BAI R,WU Y.Constructions of 3-Lie algebras[J].Linear and Multilinear Algebra,2015,63(11):2171-2186.DOI:10.1080/03081087.2014.986121.
[2]BAI C,BELLIER O,GUO L,et al.Spliting of operations,Manin products and Rota-Baxter operators[J].IMRN,2012,10:193-266.DOI:10.1093/imrn/rnr266.
[3]CARTIER P.On the structure of free Baxter algebras[J].Adv Math,1972,9:253-265.DOI:10.1016/0001-8708(72)90018-7.
[4]EBRAHIMI-FARD K,GUO L,KREIMER D.Spitzer's identity and the algebraic Birkhoff decomposition in pQFT[J].J Phys A:Math Gen,2004,37:11037-11052.DOI:10.1088/0305-4470/37/45/020.
[5]EBRAHIMI-FARD K,GUO L,MANCHON D.Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion[J].Comm Math Phys,2006,267:821-845.DOI:10.1007/s00220-00b-0080-7.
[6]BAI R,GUO L,LI Q,WU Y.Rota-Baxter 3-Lie algebras[J].J Math Phys,2013,54(6):3504.DOI:10.1063/1.4808053.
[7]BAI C,GUO L,SHENG Y.Bialgebras,the classical Yang-Baxter equation and manin triples for 3-Lie algebras[J/OL].[2017-01-03],https:/arxiv.org/:1604.0599v1[math-ph].
[8]BAI R,ZHANG Y.Homogeneous Rota-Baxter operators on 3-Lie algebra Aω[J/OL].Colloq Math,[2017-01-06],https://arxiv.org/abs/1512.02261/.DOI:10.4064/cm6829-2-2016.
[9]BAI R,ZHANG Y.Homogeneous Rota-Baxter operators on 3-Lie algebra Aω(II)[J/OL].Matp-ph.[2017-01-06],https://arxiv.org/abs/.1615.02252v2.DOI:10.4064/cm7000-4-2017.
[10]BAI R,WU Y.Constructions of 3-Lie algebras[J].Linear and Multilinear Algebra,2015,63(11):2171-2186.DOI:10.1080/03081087.2014.986121.