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

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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

DOI: https://doi.org/10.4213/faa137

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

Bibliographic databases:

UDC: 517.55+517.986

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
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• http://mi.mathnet.ru/eng/faa137
• https://doi.org/10.4213/faa137
• http://mi.mathnet.ru/eng/faa/v37/i1/p73

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Dosiev, A, “Quasispectra of solvable Lie algebra homomorphisms into Banach algebras”, Studia Mathematica, 174:1 (2006), 13
3. Pirkovskii, AY, “Arens-Michael enveloping algebras and analytic smash products”, Proceedings of the American Mathematical Society, 134:9 (2006), 2621
4. Dosiev, A, “Cartan-Slodkowski spectra, splitting elements and noncommutative spectral mapping theorems”, Journal of Functional Analysis, 230:2 (2006), 446
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
6. Dosiev, A, “Local left invertibility for operator tuples and noncommutative localizations”, Journal of K-Theory, 4:1 (2009), 163
7. Dosi, A, “Fr,chet Sheaves and Taylor Spectrum for Supernilpotent Lie Algebra of Operators”, Mediterranean Journal of Mathematics, 6:2 (2009), 181
8. A. A. Dosi, “The Taylor spectrum and transversality for a Heisenberg algebra of operators”, Sb. Math., 201:3 (2010), 355–375
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
10. Dosi A., “Taylor Functional Calculus for Supernilpotent Lie Algebra of Operators”, Journal of Operator Theory, 63:1 (2010), 191–216
11. A. Yu. Pirkovskii, “Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras”, Izv. Math., 76:4 (2012), 702–759
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
13. Pirkovskii A.Yu., “Holomorphically Finitely Generated Algebras”, J. Noncommutative Geom., 9:1 (2015), 215–264
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