Algebraic cobordism of simply connected Lie groups, by N. Yagita

Let G be a simply connected Lie group and G_C the corresponding algebraic group over the complex number field. Grothendieck and Kac showed that the Chow ring CH^*(G_C) is isomorphic to \pi^*H^*(G/T) in H^*(G) where \pi:G \to G/T is the natural projection. On the otherhand Levine and Morel recently defined the algebraic cobordism \Omega^*(X) such that \Omega^*(pt)=\Omega^*=MU^* ; the complex cobordism ring, and that \Omega^*(X)/\Omega^- = CH^*(X) for a smooth algebraic variety X over k of ch(k)=0. Let v_i be a 2(p^i-1)-dimensional ring generator in MU^*, and I=(p,v_1,...) the invariant prime ideal in MU^* for a fixed prime p. In this paper we show that the cobordism version of the Grothendieck and Kac holds with modulo I^2, namely, \Omega^*(G_C)/I^2=\pi^*(MU^*(G/T))/I^2, and compute it explicitely


N. Yagita <yagita@mito.ipc.ibaraki.ac.jp>