Minimal Matrix Representations of Decomposable Lie Algebras of Dimension Less Than or Equal to Five

doi:10.17398/2605-5686.33.2.219

Autores/as

  • Ryad Ghanam Department of Mathematics, Virginia Commonwealth University in Qatar, PO Box 8095, Doha, Qatar
  • Manoj Lamichhane Department of Mathematics, University of Wisconsin at Waukesha, Waukesha, WI 53188, U.S.A.
  • Gerard Thompson Department of Mathematics, University of Toledo, Toledo, OH 43606, U.S.A.

Palabras clave:

Lie algebra, Lie group, minimal representation

Resumen

We obtain minimal dimension matrix representations for each decomposable five-dimensional Lie algebra over R and justify in each case that they are minimal.

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Referencias

D. Burde, On a refinement of Ado’s theorem, Arch. Math. 70 (2) (1998), 118 – 127.

R. Ghanam, G. Thompson, Minimal matrix representations of four- dimensional Lie algebras, Bull. Malays. Math. Soc. (2) 36 (2) (2013), 343 – 349.

R. Ghanam, G. Thompson, Minimal matrix representations of five- dimensional Lie algebras, Extracta Math. 30 (1) (2015), 95 – 133..

G.M. Mubarakzyanov, Classification of real structures of Lie algebras of fifth order (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 3 (34) (1963), 99 – 106.

Y.-F. Kang, C.-M. Bai, Refinement of Ado’s theorem in low dimensions and applications in affine geometry, Comm. Algebra 36 (1) (2008), 82 – 93.

J. Patera, R.T. Sharp, P. Winternitz, H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Math. Phys. 17 (6) (1976), 986 – 994.

G. Thompson, Z. Wick, Subalgebras of gl(3, R), Extracta Math. 27 (2) (2012), 201 – 230.

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Publicado

2018-12-01

Número

Vol. 33 Núm. 2 (2018)

Sección

Non-associative Rings and Algebras

Cómo citar

Minimal Matrix Representations of Decomposable Lie Algebras of Dimension Less Than or Equal to Five: doi:10.17398/2605-5686.33.2.219. (2018). Extracta Mathematicae, 33(2), 219-227. https://revista-em.unex.es/index.php/EM/article/view/2605-5686.33.2.219