Abstract:We construct a certain completion $C^\infty_\mathfrak{g}$ of the universal
enveloping algebra of a triangular real Lie algebra $\mathfrak{g}$.
It is a Fréchet-Arens-Michael algebra that consists of elements
of polynomial growth and satisfies to the following universal property:
every Lie algebra homomorphism from $\mathfrak{g}$ to a real Banach algebra
all of whose elements are of polynomial growth has an extension
to a continuous homomorphism with domain $C^\infty_\mathfrak{g}$.
Elements of this algebra
can … Show more
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