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Research Article

Post-Lie algebra structures for perfect Lie algebras

Dietrich Burdea Fakultät für Mathematik, Universität Wien, Wien, AustriaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-3252-9414View further author information
ORCID Icon,
Karel Dekimpeb Katholieke Universiteit Leuven Kulak, Kortrijk, BelgiumView further author information
&
Mina Monadjema Fakultät für Mathematik, Universität Wien, Wien, AustriaView further author information
Received 18 Nov 2023, Accepted 26 Feb 2024, Published online: 15 May 2024

References

  • Alev, J., Ooms, A. I., Van den Bergh, M. (2000). The Gelfand-Kirillov conjecture for Lie algebras of dimension at most eight. J. Algebra 227(2):549–581. DOI: 10.1006/jabr.1999.8192.
  • Burde, D. (2006). Left-symmetric algebras, or pre-Lie algebras in geometry and physics. Central Eur. J. Math. 4(3):323–357.
  • Burde, D., Moens, W. A. (2007). Minimal faithful representations of reductive Lie algebras. Archiv der Math. 89(6):513–523.
  • Burde, D., Dekimpe, K., Deschamps, S. (2009). LR-algebras. Contemp. Math. 491:125–140.
  • Burde, D., Dekimpe, K., Vercammen, K. (2012). Affine actions on Lie groups and post-Lie algebra structures. Linear Algebra Appl. 437(5):1250–1263. DOI: 10.1016/j.laa.2012.04.007.
  • 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. DOI: 10.1016/j.jalgebra.2016.05.026.
  • Burde, D., Ender, C., Moens, W. A. (2018). Post-Lie algebra structures for nilpotent Lie algebras. Int. J. Algebra Comput. 28(5):915–933. DOI: 10.1142/S0218196718500406.
  • Burde, D., Gubarev, V. (2019). Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras. Commun. Algebra 47(5):2280–2296.
  • Burde, D., Gubarev, V. (2020). Decompositions of algebras and post-associative algebra structures. Int. J. Algebra Comput. 30(3):451–466. DOI: 10.1142/S0218196720500071.
  • Burde, D. (2021). Crystallographic actions on Lie groups and post-Lie algebra structures. Commun. Math. 29(1): 67–89. DOI: 10.2478/cm-2021-0003.
  • Burde, D., Dekimpe, K., Monadjem, M. (2022). Rigidity results for Lie algebras admitting a post-Lie algebra structure. Int. J. Algebra Comput. 32(08):1495–1511. DOI: 10.1142/S0218196722500679.
  • Burde, D., Moens, W. A. (2022). Semisimple decompositions of Lie algebras and prehomogeneous modules. J. Algebra 604:664–681. DOI: 10.1016/j.jalgebra.2022.04.015.
  • Ebrahimi-Fard, K., Lundervold, A., Mencattini, I., Munthe-Kaas, H. (2015). Post-Lie algebras and isospectral flows. SIGMA Symmetry Integrability Geom. Methods Appl. 11:Paper 093, 16 pp. DOI: 10.3842/SIGMA.2015.093.
  • Helmstetter, J. (1979). Radical d’une algèbre symétrique a gauche. Ann. Inst. Fourier 29:17–35. DOI: 10.5802/aif.764.
  • Turwokski, P. (1988). Low-dimensional real Lie algebras. J. Math. Phys. 29(10):2139–2144.
  • Turkowski, P. (1992). Structure of real Lie algebras. Linear Algebra Appl. 171:197–212. DOI: 10.1016/0024-3795(92)90259-D.
  • Vallette, B. (2007). Homology of generalized partition posets. J. Pure Appl. Algebra 208, no. 2 (2007), 699–725.

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