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11. A comparison of two classifications of solvable Lie algebras

Author

Saied Sorkhou, Nicolas Bryenton, Matthew Koster, Thaddeus Janisse, Yuveshen Mooroogen, Kieran Hauser, Joe Repka, Thomas Ma, Matt Wu, Arthur Rabinovich, Andrew Douglas, Jessica Liu, Saminul Haque, and Cameron Davies

Subjects
Solvable Lie algebra, Pure mathematics, 010102 general mathematics, 0103 physical sciences, Lie algebra, Statistical and Nonlinear Physics, 010307 mathematical physics, Isomorphism, 0101 mathematics, Algebra over a field, 01 natural sciences, Mathematical Physics, Mathematics
Abstract

The literature contains two different classifications of solvable Lie algebras of dimensions up to and including 4. This paper is devoted to comparing the two classifications and translating each into the other. In particular, we exhibit an isomorphism between each solvable Lie algebra of one classification and the corresponding algebra of the second. The first classification is provided by de Graaf, and the second classification is from a recent book by Snobl and Winternitz.

Published
2018
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