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Computing in groups of Lie type. (English) Zbl 1062.20049
Authors’ abstract: We describe two methods for computing with the elements of untwisted groups of Lie type: using the Steinberg presentation and using highest weight representations. We give algorithms for element arithmetic within the Steinberg presentation. Conversion between this presentation and linear representations is achieved using a new generalisation of row and column reduction.

MSC:
20G15 Linear algebraic groups over arbitrary fields
20C40 Computational methods (representations of groups) (MSC2010)
20F05 Generators, relations, and presentations of groups
68W30 Symbolic computation and algebraic computation
Software:
CHEVIE; GAP; LiE; Magma
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