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Rational G-spectra for rank 2 toral groups of mixed type

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arxiv 2501.15584 v1 pith:53SLCXSY submitted 2025-01-26 math.AT

J.P.C.Greenlees This is my paper · ORCID
classification math.AT
keywords componentg-spectrarationalsubgroupstorusactingalgebraicanalysis
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We give an explicit and calculable algebraic model for the block of rational G-spectra on full subgroups when G has identity component a 2-torus T, and component group of order 2 acting non-trivially on H_1(T). The example of particular interest is the normalizer of the maximal torus in U(2), which constitutes one of the most complicated blocks in the analysis of SU(3). This builds on the determination of subgroups up to conjugacy in arXiv 2501.06914

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rational SU(3)-equivariant cohomology theories

    math.AT 2025-02 conditional novelty 6.0 of 10

    Rational SU(3)-equivariant spectra are Quillen equivalent to differential graded objects of an explicitly constructed abelian category A(SU(3)).

  2. An algebraic model for rational U(2)-spectra

    math.AT 2025-02 conditional novelty 6.0 of 10

    The category of rational U(2)-spectra is shown to decompose into seven blocks, each with an explicit algebraic model, yielding a calculable algebraic model for the whole category.

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