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arXiv · 2511.18544

Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras

Luca Amata·Francesco Oliveri·Emanuele Sgroi
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Abstract

The complete optimal systems of subalgebras of all nonisomorphic three- and four-dimensional real Lie algebras are analyzed by the program \symbolie running in the computer algebra system \emph{Wolfram Mathematica}\texttrademark. The approach uses the definition of $p$-families of Lie subalgebras whose set can be partitioned by introducing a binary relation (reflexive and transitive, though not necessarily symmetric) induced by inner automorphisms of the Lie algebra. The results, produced in a few minutes by \symbolie, represent a good test for the program; in fact, except for minor differences that are discussed, the results confirm those given in 1977 in a paper by Patera and Winternitz.

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Luca Amata, Francesco Oliveri, Emanuele Sgroi. 2025-11-23. Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras. https://doi.org/10.46298/ocnmp.16985

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