We describe an algorithm for classifying the closed subsets of a root system, up to conjugation by the associated Weyl group. Our algorithm is implemented in the language of the computer algebra system GAP4. We discuss the implementation and give runtimes on some sample inputs. The classification of the closed subsets of an irreducible root system is closely related to the classification of the regular subalgebras, up to inner automorphism, of the corresponding simple Lie algebra. We show how to obtain the regular subalgebras corresponding to a given closed set for the root systems of rank 3. The version of this paper on the arxiv has tables describing the subalgebras that were obtained.
Closed subsets of root systems and regular subalgebras / Douglas, A.; de Graaf, W. A.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 565:(2021), pp. 531-547. [10.1016/j.jalgebra.2020.06.034]
Closed subsets of root systems and regular subalgebras
de Graaf W. A.
2021-01-01
Abstract
We describe an algorithm for classifying the closed subsets of a root system, up to conjugation by the associated Weyl group. Our algorithm is implemented in the language of the computer algebra system GAP4. We discuss the implementation and give runtimes on some sample inputs. The classification of the closed subsets of an irreducible root system is closely related to the classification of the regular subalgebras, up to inner automorphism, of the corresponding simple Lie algebra. We show how to obtain the regular subalgebras corresponding to a given closed set for the root systems of rank 3. The version of this paper on the arxiv has tables describing the subalgebras that were obtained.File | Dimensione | Formato | |
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