Skip to main content
Log in

Irreducible representations of finitely generated nilpotent torsion-free groups

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

An investigation of the structure of the quotient algebra, with respect to a prime ideal, of the group algebra of a finitely-generated nilpotent torsion-free group. Conditions are studied under which an irreducible representation of such a group is induced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. J. Dixmier, “Representations irreducible des algèbres de Lie nilpotentes,” Anais, Acad. Brasil, Ciancias,35, 491–519 (1963).

    Google Scholar 

  2. Y. Nouaze and P. Gabriel, “Idéaux premier de l'algèbre envoloppante d'une algèbre de Lie nilpotentes,” J. Algebra,6, No. 1, 77–99 (1967).

    Google Scholar 

  3. J. Dixmier, “Représentations irreductible des algèbres de Lie resolubles,” J. Math. Pures. et Appl.,45, 1–66 (1966).

    Google Scholar 

  4. A. E. Zalesskii, “Subgroups of rings without divisors of zero,” Dokl. Akad. Nauk BSSR,10, No. 10, 728–731 (1966).

    Google Scholar 

  5. P. Hall, “On the finiteness of certain soluble groups,” Proc. London Math. Soc.,9, No. 3, 595–622 (1959).

    Google Scholar 

  6. I. M. Gel'fand and A. A. Kirillow, Sur les Corps Liés aux Algèbres Enveloppantes des Algèbres de Lie, Inst. Haut. et. Sci., Publ. Math., Paris,31 (1966), pp. 509–524.

    Google Scholar 

  7. A. A. Bovdi, “Cross products of semigroups and rings,” Dokl. Akad. Nauk SSSR, 137, No. 6, 1267–1269 (1961).

    Google Scholar 

  8. O. Zarisskii and P. Samyuél, Commutative Algebra [in Russian], Vol. 1, Moscow (1963).

  9. S. D. Berman and V. V. Sharaya, Representations of one Class of Discrete Solvable Groups over an Arbitrary Algebraically Closed Field, Algebra and Mathematical Logic, Studies in Algebra, Kiev (1966), pp. 54–61.

  10. E. M. Levich, “A problem suggested by P. Hall,” Dokl. Akad. Nauk SSSR, 188, No. 6, 1241–1243 (1969).

    Google Scholar 

  11. A. E. Zalesskii, “The structure of an irreducible module over the group algebra of a polycyclic group,” Dokl. Akad. Nauk BSSR,14, No. 11, 977–980 (1970).

    Google Scholar 

  12. Dnestrovskaya Tetrad', Unsolved Problems in the Theory of Rings and Modules, Kishinev (1969).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 199–210, February, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zalesskii, A.E. Irreducible representations of finitely generated nilpotent torsion-free groups. Mathematical Notes of the Academy of Sciences of the USSR 9, 117–123 (1971). https://doi.org/10.1007/BF01316991

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01316991

Keywords

Navigation