Sheng, Yuqiu; Tang, Xiaomin Post-Lie algebra structures on the Lie algebra \(g l(2, C)\). (English) Zbl 1470.17007 Abstr. Appl. Anal. 2013, Article ID 803540, 7 p. (2013). Summary: The post-Lie algebra is an enriched structure of the Lie algebra. We give a complete classification of post-Lie algebra structures on the Lie algebra \(g l(2, C)\) up to isomorphism. Cited in 1 Document MSC: 17B30 Solvable, nilpotent (super)algebras 17A30 Nonassociative algebras satisfying other identities × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Vallette, B., Homology of generalized partition posets, Journal of Pure and Applied Algebra, 208, 2, 699-725 (2007) · Zbl 1109.18002 · doi:10.1016/j.jpaa.2006.03.012 [2] Burde, D., Left-symmetric algebras, or pre-Lie algebras in geometry and physics, Central European Journal of Mathematics, 4, 3, 323-357 (2006) · Zbl 1151.17301 · doi:10.2478/s11533-006-0014-9 [3] Burde, D.; Dekimpe, K.; Deschamps, S., LR-algebras, New Developments in Lie Theory and Geometry. New Developments in Lie Theory and Geometry, Contemporary Mathematics, 491, 125-140 (2009), Providence, RI, USA: American Mathematical Society, Providence, RI, USA · Zbl 1251.17003 · doi:10.1090/conm/491/09612 [4] Burde, D.; Dekimpe, K., Post-Lie algebra structures and generalized derivations of semisimple Lie algebras, Moscow Mathematical Journal, 13, 1, 1-18 (2013) · Zbl 1345.17011 [5] Burde, D.; Dekimpe, K.; Vercammen, K., Affine actions on Lie groups and post-Lie algebra structures, Linear Algebra and its Applications, 437, 5, 1250-1263 (2012) · Zbl 1286.17012 · doi:10.1016/j.laa.2012.04.007 [6] Loday, J.-L., Generalized bialgebras and triples of operads, Astérisque, 320 (2008) · Zbl 1178.18001 [7] Munthe-Kaas, H. Z.; Lundervold, A., On post-lie algebras, lie—butcher series and moving frames, Foundations of Computational Mathematics, 13, 4, 583-613 (2013) · Zbl 1327.17001 · doi:10.1007/s10208-013-9167-7 [8] Pan, Y.; Liu, Q.; Bai, C.; Guo, L., PostLie algebra structures on the Lie algebra \(\operatorname{ SL }(2, C)\), Electronic Journal of Linear Algebra, 23, 180-197 (2012) · Zbl 1295.17020 [9] Gantmacher, F. R., The Theory of Matrices, 2 (1959), New York, NY, USA: Chelsea Publishing, New York, NY, USA · Zbl 0085.01001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.