User:Hillgentleman/fibre functor

  • k - 係一域(field)
  • - 係對稱張量範疇(symmetric tensor category)
  • - 係k上向量空間所組成嘅範疇

定義:

A general proposition 編輯

Let

  • k - algebrically closed field, with characteristic 0
  • C - symmetric tensor category over k
    • - which is an abelian category
    • - which has finitely many indecomposable objects
  • F : C ---> Vect(k) - fibre functor
  •  
    • - the group of tensor automorphismata of F

Then

  • G is a finite group
  • C is equivalent to Rep(G), the category of representations of G.


notes 編輯


references 編輯

  • P.Etingof / O.Schiffmann (1998): "Lectures on Quantum Groups", International Press, ISBN 1571460632, p.163
  • Deligne / Milne (1982): "Tanakian Categories", Lecture Notes in Mathematics 900, [1], p.148