2025/11/23 by Amata, Luca, Oliveri, Francesco, Sgroi, Emanuele
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Finite Group Theory Research
paper · doi:10.48550/arxiv.2511.18544
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 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.