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The subalgebras of \(\mathfrak{so}(4,\mathbb C)\). (English) Zbl 1403.17005

Summary: We classify the solvable subalgebras, semisimple subalgebras, and Levi decomposable subalgebras of \(\mathfrak{so}(4,\mathbb C)\), up to inner automorphism. By Levi’s Theorem, this is a full classification of the subalgebras of \(\mathfrak{so}(4,\mathbb C)\).

MSC:

17B05 Structure theory for Lie algebras and superalgebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
17B30 Solvable, nilpotent (super)algebras

Software:

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References:

[1] Burde D., J. Lie Theory 22 (3) pp 741– (2012)
[2] DOI: 10.1016/j.jalgebra.2015.01.012 · Zbl 1354.17007 · doi:10.1016/j.jalgebra.2015.01.012
[3] DOI: 10.1063/1.4880195 · Zbl 1328.17010 · doi:10.1063/1.4880195
[4] DOI: 10.1016/j.jpaa.2013.01.010 · Zbl 1329.17009 · doi:10.1016/j.jpaa.2013.01.010
[5] DOI: 10.1063/1.4790415 · doi:10.1063/1.4790415
[6] DOI: 10.1080/10586458.2005.10128911 · Zbl 1173.17300 · doi:10.1080/10586458.2005.10128911
[7] de Graaf, W. A. (2009). SLA-computing with simple Lie algebras. A GAP package. Available at: http://www.science.unitn.it/ degraaf/sla.html.
[8] DOI: 10.1016/j.jalgebra.2010.10.021 · Zbl 1255.17007 · doi:10.1016/j.jalgebra.2010.10.021
[9] Jacobson N., Lie Algebras (1962)
[10] Minchenko, A. N. (2006). The semisimple subalgebras of exceptional Lie algebras.Trans. Moscow Math. Soc.225–259. (S 0077-1554(06)). · Zbl 1152.17003 · doi:10.1090/S0077-1554-06-00156-7
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