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The Functor \( \mathbb{C}R_{\mathbb{C}}\)

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1990)

Abstract

Let \( \mathbb{C}\) be any algebraically closed field of characteristic 0. This chapter is devoted to the study of the biset functor \( \mathbb{C}R_{\mathbb{C}}\) sending a finite group G to the \( \mathbb{C}\)-vector space \( \mathbb{C}R_{\mathbb{C}} = \mathbb{C} \otimes _{\mathbb{Z}} R_{\mathbb{C}}(G)\). This functor \( \mathbb{C}R_{\mathbb{C}}\) is defined on all finite groups, so it will be viewed as an object of \(\mathcal{F}_{\mathcal{C}, \mathbb{C}}\).

Keywords

  • Conjugacy Class
  • Galois Group
  • Cyclic Subgroup
  • Group Homomorphism
  • Primitive Character

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Correspondence to Serge Bouc .

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© 2010 Springer-Verlag Berlin Heidelberg

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Bouc, S. (2010). The Functor \( \mathbb{C}R_{\mathbb{C}}\) . In: Biset Functors for Finite Groups. Lecture Notes in Mathematics(), vol 1990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11297-3_7

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