Hodges, Timothy J. K-theory of D-modules and primitive factors of enveloping algebras of semisimple Lie algebras. (English) Zbl 0672.17008 Bull. Sci. Math., II. Sér. 113, No. 1, 85-88 (1989). Let X be a smooth quasi-projective variety over an algebraically closed field k of characteristic 0, \({\mathcal D}^ a \)sheaf of twisted differential operators over X, \({\mathcal M}({\mathcal D})\) the category of coherent left \({\mathcal D}\)-modules. It is shown that \(K_ i({\mathcal M}({\mathcal D}))\cong K_ i(X)\) for all \(i\geq 0\). It follows that if \({\mathfrak g}\) is a semisimple Lie algebra and F is a minimal primitive ideal of its enveloping algebra U(\({\mathfrak g})\) with regular central character, then \(K_ i(U({\mathfrak g})/P)\cong K_ i(G/B)\), where G/B is the associated flag variety. Reviewer: L.Vaserstein and E.Wheland Cited in 1 ReviewCited in 4 Documents MSC: 17B35 Universal enveloping (super)algebras 14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras 17B20 Simple, semisimple, reductive (super)algebras Keywords:twisted differential operators; semisimple Lie algebra; minimal primitive ideal; enveloping algebra; flag variety PDF BibTeX XML Cite \textit{T. J. Hodges}, Bull. Sci. Math., II. Sér. 113, No. 1, 85--88 (1989; Zbl 0672.17008) OpenURL