Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras
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| Format: | Preprint |
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2025
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| _version_ | 1866908715449319424 |
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| author | Amata, Luca Oliveri, Francesco Sgroi, Emanuele |
| author_facet | Amata, Luca Oliveri, Francesco Sgroi, Emanuele |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_18544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras Amata, Luca Oliveri, Francesco Sgroi, Emanuele Mathematical Physics 17B40, 35B06, 68W30 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. |
| title | Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras |
| topic | Mathematical Physics 17B40, 35B06, 68W30 |
| url | https://arxiv.org/abs/2511.18544 |