1. CJM 1998 (vol 50 pp. 816)
2. CJM 1998 (vol 50 pp. 356)
 Gross, Leonard

Some norms on universal enveloping algebras
The universal enveloping algebra, $U(\frak g)$, of a Lie algebra $\frak g$
supports some norms and seminorms that have arisen naturally in the
context of heat kernel analysis on Lie groups. These norms and seminorms
are investigated here from an algebraic viewpoint. It is shown
that the norms corresponding to heat kernels on the associated Lie
groups decompose as product norms under the natural isomorphism
$U(\frak g_1 \oplus \frak g_2) \cong U(\frak g_1) \otimes U(\frak
g_2)$. The seminorms corresponding to Green's functions are
examined at a purely Lie algebra level for $\rmsl(2,\Bbb C)$. It
is also shown that the algebraic dual space $U'$ is spanned by its
finite rank elements if and only if $\frak g$ is nilpotent.
Categories:17B35, 16S30, 22E30 
