Geodesic
Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 1, pp. 73-77.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FAA_2003_37_1_a5,
     author = {A. A. Dosiev},
     title = {Homological {Dimensions} of the {Algebra} {Formed} by {Entire} {Functions} of {Elements} of a {Nilpotent} {Lie} {Algebra}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {73--77},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2003_37_1_a5/}
}
TY  - JOUR
AU  - A. A. Dosiev
TI  - Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2003
SP  - 73
EP  - 77
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2003_37_1_a5/
LA  - ru
ID  - FAA_2003_37_1_a5
ER  - 
%0 Journal Article
%A A. A. Dosiev
%T Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2003
%P 73-77
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2003_37_1_a5/
%G ru
%F FAA_2003_37_1_a5
A. A. Dosiev. Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 1, pp. 73-77. http://geodesic.mathdoc.fr/item/FAA_2003_37_1_a5/

[1] Khelemskii A. Ya., Banakhovy i polinormirovannye algebry: obschaya teoriya, predstavleniya, gomologii, Nauka, M., 1989 | MR

[2] Dosiev A. A., “Golomorfnye funktsii ot bazisa nilpotentnoi algebry Li”, Funkts. analiz i ego pril., 34:4 (2000), 82–84 | DOI | MR | Zbl

[3] Dosiev A. A., Zapiski nauch. sem. POMI, 290, 2002, 72–121 | MR | Zbl

[4] Kaptan A., Eilenberg S., Gomologicheskaya algebra, IL, M., 1960

[5] Taylor J. L., “A general framework for a multi-operator functional calculus”, Adv. in Math., 9 (1972), 183–252 | DOI | MR | Zbl

[6] Khelemskii A. Ya., Gomologiya v banakhovykh i topologicheskikh algebrakh, MGU, M., 1986 | MR

[7] Fainshtein A. S., “Taylor joint spectrum for families of operators generating nilpotent Lie algebras”, J. Operator Theory, 29 (1993), 3–27 | MR | Zbl

[8] Dosiev A. A., “Ultraspektry predstavleniya banakhovoi algebry Li”, Funkts. analiz i ego pril., 35:4 (2001), 80–84 | DOI | MR | Zbl

[9] Dosiev A. A., “Spectra of infinite parametrized Banach complexes”, J. Operator Theory (to appear) | MR