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تسجيل مستخدم جديدAxiomatic framework for the BGG Category O
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تأليف
Apoorva Khare
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The main goal of this paper is to show that a wide variety of infinite-dimensional algebras all share a common structure, including a triangular decomposition and a theory of weights. This structure allows us to define and study the BGG Category O, generalizing previous definitions of it. Having presented our axiomatic framework, we present sufficient conditions that guarantee finite length, enough projectives, and a block decomposition into highest weight categories. The framework is strictly more general than the usual theory of O; this is needed to accommodate (quantized or higher rank) infinitesimal Hecke algebras, in addition to semisimple Lie algebras and their quantum groups. We then present numerous examples, two families of which are studied in detail. These are quantum groups defined using not necessarily the root or weight lattices (for these, we study the center and central characters), and infinitesimal Hecke algebras.
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This article aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving
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In this paper, we study the BGG category $mathcal{O}$ for the quantum Schr{o}dinger algebra $U_q(mathfrak{s})$, where $q$ is a nonzero complex number which is not a root of unity. If the central charge $dot z eq 0$, using the module $B_{dot z}$ over
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