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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...

Lie groupoids of mappings taking values in a Lie groupoid

Habib AmiriHelge GlöcknerAlexander Schmeding — 2020

Archivum Mathematicum

Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...

General Dirichlet series, arithmetic convolution equations and Laplace transforms

Helge GlöcknerLutz G. LuchtŠtefan Porubský — 2009

Studia Mathematica

In the earlier paper [Proc. Amer. Math. Soc. 135 (2007)], we studied solutions g: ℕ → ℂ to convolution equations of the form a d g d + a d - 1 g ( d - 1 ) + + a g + a = 0 , where a , . . . , a d : are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form x X f ( x ) e - s x ( s k ), where X [ 0 , ) k is an additive subsemigroup. If X is discrete and a certain solvability criterion is satisfied,...

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