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- W1672215150 abstract "We present a general setup in which one can dene an al- gebra with a regular triangular decomposition. This setup incorporates several important examples in representation theory, including semisim- ple, Kac-Moody, contragredient, and Borcherds Lie algebras, the Vi- rasoro algebra, and quantum groups. In all these cases, the Cartan subalgebra is a commutative (and mostly, also cocommutative) Hopf al- gebra; we show that this forces some of the assumptions to hold. Under one additional hypothesis, the BGG categoryO splits into blocks, each of which is a highest weight category. 1. Setup and results Given a (split) semisimple Lie algebra g, the BGG categoryO is a widely studied object in representation theory. We present an algebraic framework in which one can study the categoryO. This incorporates several well-known examples in representation theory. We work throughout over a ground eld k. All tensor products below are over k, unless otherwise specied. We dene N0 = N(f0g. Given S Z and a nite subset of an abelian groupP, the symbols ( )S stand for f( ) P 2 n : n 2 S8 g P. An associative k-algebra A is called a regular triangular algebra (de- noted also by RTA), if it has the following properties." @default.
- W1672215150 created "2016-06-24" @default.
- W1672215150 creator A5059899589 @default.
- W1672215150 date "2007-01-01" @default.
- W1672215150 modified "2023-09-27" @default.
- W1672215150 title "AXIOMATIC FRAMEWORK FOR THE BGG CATEGORY O" @default.
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