Displaying similar documents to “Serre functors for Lie algebras and superalgebras”

A remark on the Morita theorem for operads

Alexandru E. Stanculescu (2011)

Archivum Mathematicum

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We extend a result of M. M. Kapranov and Y. Manin concerning the Morita theory for linear operads. We also give a cyclic operad version of their result.

Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras

Thomas Brüstle, Lutz Hille (2000)

Colloquium Mathematicae

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Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent...

Serre Theorem for involutory Hopf algebras

Gigel Militaru (2010)

Open Mathematics

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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...