The construction and deformation of BiHom-Novikov algebras

Journal of Geometry and Physics - Tập 132 - Trang 460-472 - 2018
Shuangjian Guo1, Xiaohui Zhang2, Shengxiang Wang3
1School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, PR China
2School of Mathematical Sciences, Qufu Normal University, Qufu 273165, PR China
3School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, PR China

Tài liệu tham khảo

Balinskii, 1985, Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras, Sov. Math. Dokl., 32, 228 Dubrovin, 1983, Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method, Sov. Math. Dokl., 27, 665 Gel’fand, 1979, Hamiltonian operators and algebraic structures related to them, Funct. Anal. Appl., 13, 248, 10.1007/BF01078363 Xu, 1996, On simple Novikov algebras and their irreducible modules, J. Algebra, 185, 905, 10.1006/jabr.1996.0356 Zelmanov, 1987, On a class of local translation invariant Lie algebras, Sov. Math. Dokl., 35, 216 Filipov, 1989, A class of simple nonassociative algebras, Mat. Zametki, 45, 101 Osborn, 1992, Novikov algebras, Nova J. Algebra Geom., 1, 1 Bai, 2003, A Lie algebraic approach to Novikov algebras, J. Geom. Phys., 45, 218, 10.1016/S0393-0440(02)00150-X Auslander, 1977, Simply transitive groups of affine motions, Amer. J. Math., 99, 809, 10.2307/2373867 Bordemann, 1997, Nondegenerate invariant bilinear forms on nonassociate algebras, Acta. Math. Univ. Comenian., 66, 151 Gerstenhaber, 1964, On the deformation of rings and algebras, Ann. of Math. (2), 79, 59, 10.2307/1970484 Gerstenhaber, 1966, On the deformation of rings and algebras. II, Ann. of Math., 84, 1, 10.2307/1970528 Gerstenhaber, 1968, On the deformation of rings and algebras. III, Ann. of Math. (2), 88, 1, 10.2307/1970553 Gerstenhaber, 1974, On the deformation of rings and algebras. IV, Ann. of Math. (2), 99, 257, 10.2307/1970900 Kubo, 2004, A controlling cohomology of the deformation theory of Lie triple systems, J. Algebra, 278, 242, 10.1016/j.jalgebra.2004.01.005 Ma, 2015, One-parameter formal deformations of Hom-Lie Yamaguti algebras, J. Math. Phys., 56, 10.1063/1.4905733 B. Sun, L. Chen, Y. Liu, The construction and deformation of Hom-Novikov superalgebras, arXiv:1501.00229v1, 2015. Bai, 2001, The realization of non-transitive Novikov algebras, J. Phys. A, 34, 6435, 10.1088/0305-4470/34/33/308 Aizawa, 1991, q-deformation of the Virasoro algebra with central extension, Phys. Lett. B, 256, 185, 10.1016/0370-2693(91)90671-C Chaichian, 1990, Quantum conformal algebra with central extension, Phys. Lett. B, 248, 95, 10.1016/0370-2693(90)90021-W Hartwig, 2016, Deformations of Lie algebras using σ-derivations, J. Algebra, 295, 314, 10.1016/j.jalgebra.2005.07.036 Hu, 1999, q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebr. Colloq., 6, 51 Makhlouf, 2008, Hom-algebra structures, J. Gen. Lie Theory Appl., 2, 51, 10.4303/jglta/S070206 Makhlouf, 2009, Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras, 189 Makhlouf, 2010, Hom-algebras and Hom-coalgebras, J. Algebra Appl., 9, 553, 10.1142/S0219498810004117 Yau, 2011, Hom-Novikov algebras, J. Phys. A, 44, 10.1088/1751-8113/44/8/085202 L. Yuan, H. You, Hom-Novikov algebras and Hom-Novikov-Poisson algebras, arXiv:1204.6373. Zhang, 2011, A Hom-version of the affinizations of Balinskii-Novikov and Novikov superalgebras, J. Math. Phys., 52, 10.1063/1.3546025 Graziani, 2015, BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras, Symmetry Integrability and Geometry: Methods and Applications, 11, 1 Y. Cheng, H. Qi, Representations of BiHom-Lie algebras, arXiv:1610.04302v1, 2016. K. Abdaoui, A. Ben Hassine, A. Makhlouf, BiHom-Lie colour algebras structures, arxiv:1706.02188v1, 2017. L. Liu, A. Makhlouf, C. Menini, F. Panaite, BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota-Baxter operators on BiHom-Lie algebras, arxiv:1706.00474v1, 2017. S. Wang, S. Guo, BiHom-Lie superalgebra structures, arXiv:1610.02290v1, 2016. D. Yau, A twisted generalization of Novikov-Possion algebras, arXiv:1010.3410v1.