

Algebras in Analysis
September 28, 2018 18:05–19:35, Moscow, Lomonosov Moscow State University, room 1320.






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 ArensMchael envelope of $\mathcal A(G)$ is a homological epimorphism.
As a corollary, the solvability of a finitedimensional complex Lie algebra $\mathfrak g$ is sufficient for the ArensMichael envelope of the enveloping algebra $U(\mathfrak g)$ to be a homological epimorphism. (Pirkovskii proved earlier that this condition is necessary.)

