We illustrate the Lie theoretic capabilities of the computational algebra system GAP4 by reporting on results on nilpotent orbits of simple Lie algebras that have been obtained using computations in that system. Concerning reachable elements in simple Lie algebras we show by computational means that the simple Lie algebras of exceptional type have the Panyushev property. We computationally prove two propositions on the dimension of the abelianization of the centralizer of a nilpotent element in simple Lie algebras of exceptional type. Finally we obtain the closure ordering of the orbits in the null cone of the spinor representation of the group Spin13(C). All input and output of the relevant GAP sessions is given.
Exploring Lie theory with GAP / de Graaf, W. A.. - 783:(2023), pp. 27-46. (Intervento presentato al convegno Computational Aspects of Discrete Subgroups of Lie Groups tenutosi a Providence nel 14th-18th June 2021) [10.1090/conm/783/15698].
Exploring Lie theory with GAP
de Graaf W. A.
Primo
2023-01-01
Abstract
We illustrate the Lie theoretic capabilities of the computational algebra system GAP4 by reporting on results on nilpotent orbits of simple Lie algebras that have been obtained using computations in that system. Concerning reachable elements in simple Lie algebras we show by computational means that the simple Lie algebras of exceptional type have the Panyushev property. We computationally prove two propositions on the dimension of the abelianization of the centralizer of a nilpotent element in simple Lie algebras of exceptional type. Finally we obtain the closure ordering of the orbits in the null cone of the spinor representation of the group Spin13(C). All input and output of the relevant GAP sessions is given.File | Dimensione | Formato | |
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