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Shifted functors of linear representations are semisimple

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Abstract

We prove that, for any fields k and \(\mathbb {F}\) of characteristic 0 and any finite group T, the category of modules over the shifted Green biset functor \((kR_{\mathbb {F}})_T\) is semisimple.

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References

  1. Alperin, J.L., Bell, R.B.: Groups and Representations, Graduate Texts in Mathematics, vol. 162. Springer, New York (1995)

  2. Anderson, F.W., Fuller, K.R.: Rings and categories of modules, Graduate Texts in Mathematics, vol. 13, 2nd edn. Springer, New York (1992)

  3. Barker, L.: Rhetorical biset functors, rational \(p\)-biset functors and their semisimplicity in characteristic zero. J. Algebra 319, 3810–3853 (2008)

    Article  MathSciNet  Google Scholar 

  4. Bouc, S.: Biset Functors for Finite Groups. Springer, Berlin (2010)

    Book  Google Scholar 

  5. Bouc, S., Romero, N.: The center of a Green biset functors. Pac. J. Math. 303, 459–490 (2019)

    Article  MathSciNet  Google Scholar 

  6. Curtis, C., Reiner, I.: Methods of Representation Theory with Applications to Finite Groups and Orders, vol. 1. Wiley, New York (1981)

    MATH  Google Scholar 

  7. García, B.: Construcción de Yoneda-Dress de funtores de representaciones lineales. Tesis de Doctorado UMSNH-UNAM, Morelia (2018)

    Google Scholar 

  8. García, B.: On the ideals and essential algebras of shifted functors of linear representations. J. Algebra 521, 452–480 (2019)

    Article  MathSciNet  Google Scholar 

  9. Romero, N.: Simple modules over Green biset functors. J. Algebra 367, 203–221 (2012)

    Article  MathSciNet  Google Scholar 

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Correspondence to Nadia Romero.

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Bouc, S., Romero, N. Shifted functors of linear representations are semisimple. Math. Z. 300, 247–257 (2022). https://doi.org/10.1007/s00209-021-02790-y

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  • DOI: https://doi.org/10.1007/s00209-021-02790-y

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