Algebras whose groups of units are Lie groups

• Autorzy: Helge Glöckner
• Języki publikacji: EN

Abstrakty

EN

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 a globally defined exponential function. We also discuss generalizations in the setting of "convenient differential calculus", and describe various examples.

Kategorie tematyczne

• 46H30: Functional calculus in topological algebras
• 46E25: Rings and algebras of continuous, differentiable or analytic functions
• 46H05: General theory of topological algebras
• 46F05: Topological linear spaces of test functions, distributions and ultradistributions
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 153
• Numer: 2
• Strony: 147-177

Daty

wydano

2002

Twórcy

autor

Helge Glöckner

• FB Mathematik, TU Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany

Identyfikatory

DOI

10.4064/sm153-2-4