Arens–Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms
Copyright policy )Arens–Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms
Our aim is to give an explicit description of the Arens-Michael envelope for the universal enveloping algebra of a finite-dimensional nilpotent complex Lie algebra. It turns out that the Arens-Michael envelope belongs to a class of completions introduced by R.~Goodman in 70s. To find a precise form of this algebra we preliminary characterize the set of holomorphic functions of exponential type on a simply connected nilpotent complex Lie group. This approach leads to unexpected connections to Riemannian geometry and the theory of order and type for entire functions. As a corollary, it is shown that the Arens-Michael envelope considered above is a homological epimorphism. So we get a positive answer to a question investigated earlier by Dosi and Pirkovskii.
18 pages
- Lomonosov Moscow State University Russian Federation
Solvable, nilpotent (super)algebras, Nilpotent and solvable Lie groups, Topological linear spaces of test functions, distributions and ultradistributions, Arens-Michael envelope, submultiplicative weight, holomorphic function of exponential type, Functional Analysis (math.FA), Mathematics - Functional Analysis, Analysis on real and complex Lie groups, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), length function, homological epimorphism, FOS: Mathematics, Universal enveloping (super)algebras, Algebras of holomorphic functions of several complex variables, nilpotent Lie algebra
Solvable, nilpotent (super)algebras, Nilpotent and solvable Lie groups, Topological linear spaces of test functions, distributions and ultradistributions, Arens-Michael envelope, submultiplicative weight, holomorphic function of exponential type, Functional Analysis (math.FA), Mathematics - Functional Analysis, Analysis on real and complex Lie groups, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), length function, homological epimorphism, FOS: Mathematics, Universal enveloping (super)algebras, Algebras of holomorphic functions of several complex variables, nilpotent Lie algebra
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