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Research Article

Invariant metrics on current Lie algebras

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Pages 5332-5343 | Received 09 Mar 2023, Accepted 22 Jun 2023, Published online: 11 Jul 2023

References

  • Bajo, I., Benayadi, S. (2007). Lie algebras with quadratic dimension equal to 2. J. Algebra 29(3):725–737. DOI: 10.1016/j.jpaa.2006.07.010.
  • Chaktoura, M., Szechtman, F. A note on orthogonal Lie algebras in dimension 4 viewed as a current Lie algebras. https://arxiv.org/pdf/1306.4006.pdf
  • Duong, M. T., Pinczon, G., Ushirobira, R. (2012). A new invariant of quadratic Lie algebras. Algebra Representation Theory 15:1163–1203. DOI: 10.1007/s10468-011-9284-4.
  • Humphreys, J. E. (1972). Introduction to Lie Algebras and Representation Theory. New York: Springer Verlag. DOI: 10.1007/978-1-4612-6398-2.
  • Kath, I., Olbrich, M. (2006). Metric Lie algebras and quadratic extensions. Transform. Groups 11:87–131. DOI: 10.1007/s00031-005-1106-5.
  • Medina, A., Revoy, P. (1985). Algebres de Lie et produit scalare invariant. Ann. Scient. Ec. Norm. Sup. 18:553–561. DOI: 10.24033/asens.1496.
  • Ochoa, J., Rojas, N. (2019). The Lie algebra of derivations of a current Lie algebra. Commun. Algebra 48(2):625–637. DOI: 10.1080/00927872.2019.1654490.
  • Rodríguez-Vallarte, M. C., Salgado, G., Sánchez-Valenzuela, O. A. (2011). Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms. J. Algebra 331(1):71–86. DOI: 10.1016/j.jalgebra.2011.02.003.
  • Cagliero, L., Rojas, N. (2009). Faithful representations of minimal dimension of current Heisenberg Lie algebras. Int. J. Math. 20(11):1347–1362. DOI: 10.1142/S0129167X09005790.
  • Remm, E., Goze, M. (2014). Rigid current Lie algebras. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A., eds. Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, Vol. 85. Heidelberg: Springer, pp. 247–258. DOI: 10.1007/978-3-642-55361-5_14.
  • Zhu, L., Meng, D. (2001). Quadratic Lie algebras and commutative associative Lie algebras. Commun. Algebra 29(5):2249–2268. DOI: 10.1081/AGB-100002182.

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