References
- Abdaoui, E., Mabrouk, S., Makhlouf, A. (2019). Rota-Baxter operators on pre-Lie superalgebras. Bull. Malays. Math. Sci. Soc. 42(4):1567–1606.
- An, H., Bai, C. (2008). From Rota-Baxter algebras to pre-Lie algebras. J. Phys. A. 41(1):19.
- Bai, C. (2006). A further study on non-abelian phase spaces: left-symmetric algebraic approach and related geometry. Rev. Math. Phys. 18(5):545–564.
- Bai, C. (2007). A unified algebraic approach to the classical Yang-Baxter equation. J. Phys. A. 40(36):11073–11082.
- Bai, C., Bellier, O., Guo, L., Ni, X. (2013). Splitting of operations, Manin products, and Rota-Baxter operators. Int. Math. Res. Not. IMRN. 2013(3):485–524.
- Bai, C., Guo, L., Sheng, Y. (2019). Bialgebras, the classical Yang-Baxter equations and Manin triples for 3-Lie algebras. Adv. Theor. Math. Phys. 23:27–74.
- Bai, R., Guo, L., Li, J., Wu, Y. (2013). Rota-Baxter 3-Lie algebras. J. Math. Phys. 54(6):14.
- Baxter, G. (1960). An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. 10:731–742.
- Benito, P., Bremner, M., Madariaga, S. (2015). Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras. Linear Multilinear Algebra 63(6):1257–1281.
- Benito, P., Draper, C., Elduque, A. (2005). Lie-Yamaguti algebras related to g2. J. Pure Appl. Algebra 202(1-3):22–54.
- Benito, P., Elduque, A., Martin-Herce, F. (2009). Irreducible Lie-Yamaguti algebras. J. Pure Appl. Algebra 213(5):795–808.
- Benito, P., Elduque, A., Martin-Herce, F. (2011). Irreducible Lie-Yamaguti algebras of generic type. J. Pure Appl. Algebra 215(2):108–130.
- Burde, D. (2006). Left-symmetric algebras and pre-Lie algebras in geometry and physics, Cent. Eur. J. Math. 4:323–357.
- Chari, V., Pressley, A. (1994). A Guide to Quantum Groups. Cambridge: Cambridge University Press.
- Guo, L. (2012). An introduction to Rota-Baxter algebra. Surveys of Modern Mathematics, 4. International Press, Somerville, MA; Higher Education Press, Beijing, pp. xii+226.
- Hou, S., Sheng, Y., Tang, R. (2021). Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators. J. Geom. Phys. 163:104148.
- Jacobson, N. (1949). Lie and Jordan triple systems. Amer. J. Math. 71:149–170.
- Kikkawa, M. (1981). On Killing-Ricci forms of Lie triple algebras. Pacific J. Math. 96(1):153–161.
- Kinyon, M., Weinstein, A. (2001). Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces. Am. J. Math. 123(3):525–550.
- Kupershmidt, B. A. (1999). What a classical r-matrix really is. J. Nonlinear Math. Phys. 6(4):448–488.
- Lin, J., Chen, L., Ma, Y. (2015). On the deformation of Lie-Yamaguti algebras. Acta Math. Sin. (Engl. Ser.). 31(6):938–946.
- Lin, J., Wang, Y., Deng, S. (2009). T*-extension of Lie triple systems. Linear Algebra Appl. 431(11):2071–2083.
- Lister, W. G. (1952). A structure theory of Lie triple systems. Trans. Am. Math. Soc. 72:217–242.
- Mabrouk, S. Pre-Lie triple systems structures and generalized derivations. DOI: 10.13140/RG.2.2.25897.93283.
- Nomizu, K. (1954). Invariant affine connections on homogeneous spaces. Am. J. Math. 76:33–65.
- Pei, J., Bai, C., Guo, L. (2017). Splitting of operads and Rota-Baxter operators on operads. Appl. Categ. Structures 25(4):505–538.
- Semonov-Tian-Shansky, M. A. (1983). What is a classical R-matrix? Funct. Anal. Appl. 17:259–272.
- Sheng, Y., Zhao, J., Zhou, Y. (2021). Nijnhuis operators, product structures and complex structures on Lie-Yamaguti algebras. J. Algebra Appl. 20(8):22. pp. 2150146.
- Takahashi, N. Modules over quadratic spaces and representations of Lie-Yamaguti algebras. arXiv:2010.05564.
- Tang, R., Hou, S., Sheng, Y. (2021). Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras. J. Algebra 567:37–62.
- Yamaguti, K. (1957/58). On the Lie triple system and its generalization. J. Sci. Hiroshima Univ. Ser. A 21:155–160.
- Yamaguti, K. (1967/69). On cohomology groups of general Lie triple systems. Kumamoto J. Sci. Ser. A 8:135–146.
- Yamaguti, K. (1960). On the cohomology space of Lie triple system. Kumamoto J. Sci. Ser. A 5:44–52.
- Zhang, T., Li, J. (2015). Deformations and extensions of Lie-Yamaguti algebras. Linear Multilinear Algebra 63(11):2212–2231.