Borel subalgebras redux with examples from algebraic and quantum groups (Q1841203)

This paper formulates a general notion of a Borel subalgebra of a quasi-hereditary algebra. The approach is categorical, through highest weight categories. Many examples are treated. We meet classical and generalized \(q\)-Schur algebras, graded Kazhdan-Lusztig theories, Frobenius kernels, representations arising from Schubert varieties. Various kinds of Borel subalgebras are introduced: exact, homological, excellent. A comparison is made with earlier definitions by \textit{J. A. Green} [J. Algebra 131, No. 1, 265-280 (1990; Zbl 0715.20025)] and \textit{S. König} [in R. Bautista (ed.) et al., Representation theory of algebras. Seventh international conference, August 22-26, 1994, Cocoyoc, Mexico. Providence, RI: American Mathematical Society. CMS Conf. Proc. 18, 399-417 (1996; Zbl 0852.16006)]. In the first printing the paper is hard to decrypt, as all minus signs have been rendered as spaces. Therefore there is a second printing.