Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Stably flat completions of universal enveloping algebras

100%

Pirkovskii A.

Instytut Matematyczny Polskiej Akademii Nauk

Let 𝔤 be a complex Lie algebra, and let U(𝔤) be its universal enveloping algebra. We study homological properties of topological Hopf algebras containing U(𝔤) as a dense subalgebra. Specifically, let θ: U(𝔤) → H be a homomorphism to a topological Hopf algebra H. Assuming that H is either a nuclear Fréchet space or a nuclear (DF)-space, we formulate conditions on the dual algebra, H', that are sufficient for H to be stably flat over U(𝔤) in the sense of A. Neeman and A. Ranicki (2001) (i.e., for θ to be a localization in the sense of J. L. Taylor (1972)). As an application, we prove that the Arens-Michael envelope, Ũ(𝔤), of U(𝔤) is stably flat over U(𝔤) provided 𝔤 admits a positive grading. We also show that R. Goodman's (1979) weighted completions of U(𝔤) are stably flat over U(𝔤) for each nilpotent Lie algebra 𝔤, and that P. K. Rashevskii's (1966) hyperenveloping algebra is stably flat over U(𝔤) for any 𝔤. Finally, the algebra 𝓐(G) of analytic functionals (introduced by G. L. Litvinov (1969)) on the corresponding connected, simply connected complex Lie group G is shown to be stably flat over U(𝔤) precisely when 𝔤 is solvable.

On Arens-Michael algebras which do not have non-zero injective ⨶-modules

96%

Pirkovskii A.

Studia Mathematica

1999

tom 133

nr 2

163-174

A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in $ℂ^n$, algebras of smooth functions on domains in $ℝ^n$, algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.

Ograniczanie wyników

1 Studia Mathematica

2 Pirkovskii A.

1 2006

1 1999

Wyniki wyszukiwania

Stably flat completions of universal enveloping algebras

On Arens-Michael algebras which do not have non-zero injective ⨶-modules