Effective algorithms for groups of lie type

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Project objective

The groups of Lie type are among the most important structures in modern mathematics. They also have many applications to physics. This project will construct algorithms for computing with elements and subgroups of these groups. We will concentrate on the following structural properties: automorphisms and twisted groups, conjugacy classes, and maximal subgroups. Our approach is designed to make the underlying Lie theory explicit, by using the Steinberg presentation as our starting point. We have already designed an effective correspondence between the Steinberg presentation and the more traditional matrix representations. The research content of the project will primarily be the creation of classification theorems for the structural properties that are suitable for computation, building on existing classifications. We will implement our algorithms in GAP and Magma so as to make them available to the wider scientific community . This work will complement the Chevie project, which has already made computational Lie theory one of the strengths of European mathematics.

Original text from CORDIS.

Participants

• EINDHOVEN UNIVERSITY OF TECHNOLOGY · EINDHOVENCoordinatorNetherlands

Links

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