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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 1, Pages 73–77 (Mi faa137)  

This article is cited in 13 scientific papers (total in 13 papers)

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Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra

A. A. Dosiev

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: This note deals with homological characteristics of algebras of holomorphic functions of noncommuting variables generated by a finite-dimensional nilpotent Lie algebra $\mathfrak{g}$. It is proved that the embedding $\mathcal{U}(\mathfrak{g})\to\mathcal{O}_{\mathfrak{g}}$ of the universal enveloping algebra $\mathcal{U}(\mathfrak{g})$ of $\mathfrak{g}$ into its Arens–Michael hull $\mathcal{O}_{\mathfrak{g}}$ is an absolute localization in the sense of Taylor provided that $[\mathfrak{g},[\mathfrak{g},\mathfrak{g}]]=0$.

Keywords: Arens–Michael hull, projective homological dimension, nilpotent Lie algebra, localization, Taylor spectrum


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English version:
Functional Analysis and Its Applications, 2003, 37:1, 61–64

Bibliographic databases:

UDC: 517.55+517.986
Received: 23.11.2001

Citation: A. A. Dosiev, “Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 73–77; Funct. Anal. Appl., 37:1 (2003), 61–64

Citation in format AMSBIB
\by A.~A.~Dosiev
\paper Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra
\jour Funktsional. Anal. i Prilozhen.
\yr 2003
\vol 37
\issue 1
\pages 73--77
\jour Funct. Anal. Appl.
\yr 2003
\vol 37
\issue 1
\pages 61--64

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    This publication is cited in the following articles:
    1. A. A. Dosiev, “Cohomology of Sheaves of Fréchet Algebras and Spectral Theory”, Funct. Anal. Appl., 39:3 (2005), 225–228  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Dosiev, A, “Quasispectra of solvable Lie algebra homomorphisms into Banach algebras”, Studia Mathematica, 174:1 (2006), 13  crossref  mathscinet  zmath  isi  scopus
    3. Pirkovskii, AY, “Arens-Michael enveloping algebras and analytic smash products”, Proceedings of the American Mathematical Society, 134:9 (2006), 2621  crossref  mathscinet  zmath  isi  scopus
    4. Dosiev, A, “Cartan-Slodkowski spectra, splitting elements and noncommutative spectral mapping theorems”, Journal of Functional Analysis, 230:2 (2006), 446  crossref  mathscinet  zmath  isi  scopus
    5. A. A. Dosi, “Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem”, Izv. Math., 73:6 (2009), 1149–1171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Dosiev, A, “Local left invertibility for operator tuples and noncommutative localizations”, Journal of K-Theory, 4:1 (2009), 163  crossref  mathscinet  zmath  isi  scopus
    7. Dosi, A, “Fr,chet Sheaves and Taylor Spectrum for Supernilpotent Lie Algebra of Operators”, Mediterranean Journal of Mathematics, 6:2 (2009), 181  crossref  mathscinet  zmath  isi  scopus
    8. A. A. Dosi, “The Taylor spectrum and transversality for a Heisenberg algebra of operators”, Sb. Math., 201:3 (2010), 355–375  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Dosi A., “Formally-radical Functions in Elements of a Nilpotent Lie Algebra and Noncommutative Localizations”, Algebra Colloq, 17, Sp. Iss. 1 (2010), 749–788  crossref  mathscinet  zmath  isi  elib
    10. Dosi A., “Taylor Functional Calculus for Supernilpotent Lie Algebra of Operators”, Journal of Operator Theory, 63:1 (2010), 191–216  mathscinet  zmath  isi
    11. A. Yu. Pirkovskii, “Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras”, Izv. Math., 76:4 (2012), 702–759  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Pirkovskii A.Yu., “Noncommutative Analogues of Stein Spaces of Finite Embedding Dimension”, Algebraic Methods in Functional Analysis: the Victor Shulman Anniversary Volume, Operator Theory Advances and Applications, 233, ed. Todorov I. Turowska L., Birkhauser Verlag Ag, 2014, 135–153  crossref  mathscinet  zmath  isi  scopus
    13. Pirkovskii A.Yu., “Holomorphically Finitely Generated Algebras”, J. Noncommutative Geom., 9:1 (2015), 215–264  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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