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Homological dimensions of smooth and complex analytic quantum tori
A. Yu. Pirkovskii
We survey some results on homological dimensions of the algebraic, complex analytic, and smooth quantum tori. Our main theorem states, in particular, that the smooth and the comple…
Homological dimensions of K"othe algebras
A. Yu. Pirkovskii
Given a metrizable K"othe algebra , we compute the global dimension, the weak global dimension, the bidimension, and the weak bidimension of in terms of the K"othe set…
Flat cyclic Fréchet modules, amenable Fréchet algebras, and approximate identities
A. Yu. Pirkovskii
Let A be a locally m-convex Fréchet algebra. We give a necessary and sufficient condition for a cyclic Fréchet A-module X=A_+/I to be strictly flat, generalizing thereby a criterio…
Strictly flat cyclic Fréchet modules and approximate identities
A. Yu. Pirkovskii
Let A be a locally m-convex Fréchet algebra. We give a necessary and sufficient condition for a cyclic Fréchet A-module X=A_+/I to be strictly flat, generalizing thereby a criterio…
Arens-Michael enveloping algebras and analytic smash products
A. Yu. Pirkovskii
Let g be a finite-dimensional complex Lie algebra, and let U(g) be its universal enveloping algebra. We prove that if \hat{U}(g), the Arens-Michael envelope of U(g), is stably flat…
Biprojectivity and biflatness for convolution algebras of nuclear operators
A. Yu. Pirkovskii
For a locally compact group G, the convolution product on the space N(L^p(G)) of nuclear operators was defined by Neufang. We study homological properties of the convolution algebr…