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Serre Theorem for involutory Hopf algebras

100%

Militaru G.

Open Mathematics

2010

tom 8

nr 1

15-21

We call a monoidal category C a Serre category if for any C, D ∈ C such that C ⊗ D is semisimple, C and D are semisimple objects in C. Let H be an involutory Hopf algebra, M, N two H-(co)modules such that M ⊗ N is (co)semisimple as a H-(co)module. If N (resp. M) is a finitely generated projective k-module with invertible Hattory-Stallings rank in k then M (resp. N) is (co)semisimple as a H-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel’d modules over H the dimension of which are invertible in k are Serre categories.

Categorification of Hopf algebras of rooted trees

75%

Kock J.

Open Mathematics

2013

tom 11

nr 3

401-422

We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring in the polynomial representation of the free monad on P.

Ograniczanie wyników

2 Open Mathematics

1 Kock J.

1 Militaru G.

1 2013

1 2010

Wyniki wyszukiwania

Serre Theorem for involutory Hopf algebras

Categorification of Hopf algebras of rooted trees