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Full-Text Articles in Physical Sciences and Mathematics
Rank Reduction Of String C-Group Representations, Peter A. Brooksbank, Dimitri Leemans
Rank Reduction Of String C-Group Representations, Peter A. Brooksbank, Dimitri Leemans
Faculty Journal Articles
We show that a rank reduction technique for string C-group representations first used in [Adv. Math. 228 (2018), pp. 3207–3222] for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on d-dimensional modules over fields of even order greater than 2 possess string C-group representations of all ranks. The broad applicability of the rank reduction technique provides fresh impetus to construct, for suitable families of groups, string C-groups of highest possible rank. It also suggests that the alternating group Alt(11)—the only known group having “rank gaps”—is perhaps more unusual …
Testing Isomorphism Of Graded Algebras, Peter A. Brooksbank, James B. Wilson, Eamonn A. O'Brien
Testing Isomorphism Of Graded Algebras, Peter A. Brooksbank, James B. Wilson, Eamonn A. O'Brien
Faculty Journal Articles
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma.