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Algebraic loop groups and moduli spaces of bundles

Gerd Faltings (2003)

Journal of the European Mathematical Society

We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.

Algebras whose groups of units are Lie groups

Helge Glöckner (2002)

Studia Mathematica

Let A be a locally convex, unital topological algebra whose group of units A × is open and such that inversion ι : A × A × is continuous. Then inversion is analytic, and thus A × is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then A × has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group A × is an analytic Lie group without...

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