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• # Artykuł - szczegóły

## Studia Mathematica

2002 | 153 | 2 | 147-177

## Algebras whose groups of units are Lie groups

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### 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.

147-177

wydano
2002

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