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Original Article

Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras

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Pages 2280-2296 | Received 18 May 2018, Accepted 01 Oct 2018, Published online: 11 Jan 2019

References

  • Atkinson, F. V. (1963). Some aspects of Baxters functional equation. J. Math. Anal. Appl. 7(1): 1–30.
  • Bai, C., Guo, L., Ni, X. (2010). Nonabelian generalized lax pairs, the classical Yang-Baxter equation and PostLie algebras. Commun. Math. Phys. 297(2):553–596.
  • Baxter, G. (1960). An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. 10(3):731–742.
  • Belavin, A. A., Drinfel'd, V. G. (1983). Solutions of the classical Yang-Baxter equation for simple Lie algebras. Funct. Anal. Appl. 16(3):159–180.
  • Benito, P., Gubarev, V., Pozhidaev, A. (2018). Rota–Baxter operators on quadratic algebras. 23. arXiv:1801.07037
  • Burde, D. (1996). Affine structures on nilmanifolds. Int. J. Math. 07(05):599–616.
  • Burde, D., Dekimpe, K., Deschamps, S. (2005). The Auslander conjecture for NIL-affine crystallographic groups. Math. Ann. 332(1):161–176.
  • Burde, D. (2006). Left-symmetric algebras, or pre-Lie algebras in geometry and physics. Centr. Eur. J. Math. 4(3):323–357.
  • Burde, D., Dekimpe, K., Deschamps, S. (2009). LR-algebras. Contemp. Math. 491:125–140.
  • Burde, D., Dekimpe, K., Vercammen, K. (2010). Complete LR-structures on solvable Lie algebras. J. Group Theory. 13(5):703–719.
  • Burde, D., Dekimpe, K., Vercammen, K. (2012). Affine actions on Lie groups and post-Lie algebra structures. Linear Algebra Appl. 437(5):1250–1263.
  • Burde, D., Dekimpe, K. (2013). Post-Lie algebra structures and generalized derivations of semisimple Lie algebras. Mosc. Math. J. 13(1):1–18.
  • Burde, D., Dekimpe, K. (2016). Post-Lie algebra structures on pairs of Lie algebras. J. Algebra. 464:226–245.
  • Burde, D., Moens, W. A. (2016). Commutative post-Lie algebra structures on Lie algebras. J. Algebra. 467:183–201.
  • Burde, D., Moens, W. A., Dekimpe, K. (2017). Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras. 1–14. arXiv:1711.01964
  • Cartier, P. (1972). On the structure of free Baxter algebras. Adv. Math. 9(2):253–265.
  • Douglas, A., Repka, J. (2018). Subalgebras of the rank two semisimple Lie algebras. Linear Multilinear Algebra. 66(10):2049–2075.
  • Ebrahimi-Fard, K., Lundervold, A., Mencattini, I., Munthe-Kaas, H. Z. (2015). Post-Lie algebras and isospectral flows. SIGMA Symmetry Integrability Geom. Methods Appl. 11(93):16.
  • Gubarev, V. (2017). Universal enveloping Lie Rota–Baxter algebra of pre-Lie and post-Lie algebras. 1–13. arXiv:1708.06747
  • Gubarev, V., Kolesnikov, P. (2013). Embedding of dendriform algebras into Rota–Baxter algebras. Cent. Eur. J. Math. 11(2):226–245.
  • Guo, L., Keigher, W. (2000). Baxter algebras and shuffle products. Adv. Math. 150(1):117–149.
  • Guo, L. (2012). An Introduction to Rota–Baxter Algebra. Surveys of Modern Mathematics, Vol. 4. Somerville: Intern. Press, 226 pp.
  • Helmstetter, J. (1979). Radical d’une algèbre symétrique a gauche. Ann. Inst. Fourier. 29(4):17–35.
  • Jacobson, N. (1962). A note on automorphisms of Lie algebras. Pacific J. Math. 12(1):303–315.
  • Li, X. X., Hou, D. P., Bai, C. M. (2007). Rota–Baxter operators on pre-Lie algebras. J. Nonlinear Math. Phys. 14(2):269–289.
  • Kim, H. (1986). Complete left-invariant affine structures on nilpotent Lie groups. J. Differential Geom. 24(3):373–394.
  • Koszul, J. L. (1978). Variante d’un théoréme de H. Ozeki. Osaka J. Math. 15:547–551.
  • Loday, J.-L. (2008). Generalized bialgebras and triples of operads. Astrisque No. 320:116.
  • Onishchik, A. L. (1969). Decompositions of reductive Lie groups. Mat. Sbornik. 80(122):515–554.
  • Rota, G.-C. (1969). Baxter algebras and combinatorial identities I. Bull. Am. Math. Soc. 75(2):325–329.
  • Schafer, R. D. (1995). An Introduction to Nonassociative Algebras. New York, NY: Dover Publications, 166 pp.
  • Segal, D. (1992). The structure of complete left-symmetric algebras. Math. Ann. 293(1):569–578.
  • Semenov-Tyan-Shanskii, M. A. (1983). What is a classical R-matrix? Funktsional. Anal. i Prilozhen. 17(4):17–33.
  • Vallette, B. (2007). Homology of generalized partition posets. J. Pure Appl. Algebra. 208(2):699–725.