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On weak i -homotopy equivalences of modules

Zheng-Xu He (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si definisce il gruppo di i —omotopia di un singolo modulo e si introduce la nozione di equivalenza i -omotopica debole. Sotto determinate condizioni per l'anello di base Λ oppure per i moduli considerati, le equivalenze i -omotopiche deboli coincidono con le equivalenze i -omotopiche (forti).

Serre functors for Lie algebras and superalgebras

Volodymyr Mazorchuk, Vanessa Miemietz (2012)

Annales de l’institut Fourier

We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category 𝒪 associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category 𝒪 and its parabolic generalizations for classical Lie superalgebras are categories with full projective functors. As an application we prove that in many cases the endomorphism algebra of the basic...

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