We show that the category of partial comodules over a Hopf algebra H is comonadic over Vect k and provide an explicit construction of this comonad using topological vector spaces. The case when H is finite dimensional is treated in detail. A study of partial representations of linear algebraic groups is initiated; we show that a connected linear algebraic group does not admit partiality.
Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case H = {1 G }), we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group Sn and its subgroup S n−1 of permutations fixing 1: this provides a natural extension of the classical representation theory of Sn.
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