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Algebras in Analysis
September 28, 2018 18:05–19:35, Moscow, Lomonosov Moscow State University, room 13-20.
 


Universal enveloping algebras, analytic functionals, and homological epimorphisms

O. Yu. Aristov

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Abstract: We discuss homological properties of the algebra $\mathcal A(G)$ of analytic functionals on a complex Lie group $G$. We show that
(1) If $G$ is linearly complex reductive (for example, semisimple) and connected, then $\mathcal A(G)$ is homologically trivial.
(2) For each connected $G$ the Arens-Mchael envelope of $\mathcal A(G)$ is a homological epimorphism.
As a corollary, the solvability of a finite-dimensional complex Lie algebra $\mathfrak g$ is sufficient for the Arens-Michael envelope of the enveloping algebra $U(\mathfrak g)$ to be a homological epimorphism. (Pirkovskii proved earlier that this condition is necessary.)

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