On *-modules generating the injectives
Si definisce il gruppo di —omotopia di un singolo modulo e si introduce la nozione di equivalenza -omotopica debole. Sotto determinate condizioni per l'anello di base oppure per i moduli considerati, le equivalenze -omotopiche deboli coincidono con le equivalenze -omotopiche (forti).
We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category 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 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...
By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule . We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra...