The subalgebras of the rank two symplectic Lie algebra

The semisimple subalgebras of the rank 2 symplectic Lie algebra sp(4,C) are well-known, and we recently classified its Levi decomposable subalgebras. In this article, we classify the solvable subalgebras of sp(4,C), up to inner automorphism. This completes the classification of the subalgebras of sp...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 527; pp. 303 - 348
Main Authors Douglas, Andrew, Repka, Joe
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.08.2017
American Elsevier Company, Inc
Subjects
Algebra
Automorphisms
Classification
Classification of subalgebras
Lie groups
Linear algebra
Mathematics
Symplectic algebra
Symplectic algebra
Classification of subalgebras
17B30
17B05
17B20
17B10
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Summary:The semisimple subalgebras of the rank 2 symplectic Lie algebra sp(4,C) are well-known, and we recently classified its Levi decomposable subalgebras. In this article, we classify the solvable subalgebras of sp(4,C), up to inner automorphism. This completes the classification of the subalgebras of sp(4,C). More broadly speaking, in completing the classification of the subalgebras of sp(4,C) we have completed the classification of the subalgebras of the rank 2 semisimple Lie algebras.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.03.031