ISSN:
1573-0530
Keywords:
Primary 22E65
;
Secondary 20E18, 20F40
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract A direct limit $$G = \mathop {\lim }\limits_ \to G_\alpha$$ of (finite-dimensional) Lie groups has Lie algebra $$\mathfrak{g} = \mathop {\lim }\limits_ \to \mathfrak{g}_\alpha$$ and exponential map exp G : g→G. BothG and g carry natural topologies.G is a topological group, and g is a topological Lie algebra with a natural structure of real analytic manifold. In this Letter, we show how a special growth condition, natural in certain physical settings and satisfied by the usual direct limits of classical groups, ensures thatG carries an analytic group structure such that exp G is a diffeomorphism from a certain open neighborhood of 0∈g onto an open neighborhood of 1 G ∈G. In the course of the argument, one sees that the structure sheaf for this analytic group structure coincides with the direct limit $$\mathop {\lim }\limits_ \to$$ C ω(G α) of the sheaves of germs of analytic functions on theG α.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00703721
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