engleski

Actions of monoidal categories which represent actions in noncommutative geometry

In a number of examples studied in noncommutative geometry, Hopf algebras appear as symmetries of noncommutative spaces. Actions and coactions of Hopf algebras on noncommutative algebras were studied in past. In this talk I will explain how to extend such "affine" examples to nonaffine examples where the noncommutative algebra acted upon is replaced by some category "of (quasi)coherent sheaves" and the Hopf algebra in Tannakian spirit by a monoidal category. The relative setup forces an appearance of distributive laws, in particular those distributive laws which are named "entwining structures", and many other examples. Notions of equivariant sheaves and a natural setup for torsors and stack-like noncommutative quotients will also be presented in this generality.

monoidal category; action; equivariant sheaf; noncommutative geometry; Hopf algebra

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