Skip to main content

On the laws of finite dimensional representations of solvable lie algebras and groups

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1352))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Yu.P. Razmyslov. Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero (in Russian). Algebra Logika 12 (1973), 83–113. (English translation: Algebra Logic, 12 (1973), 47–63 (1974)).

    Article  MathSciNet  Google Scholar 

  2. Hanna Neumann. Varieties of groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37. Springer-Verlag, 1967.

    Google Scholar 

  3. Yu.A. Bahturin. Lectures on Lie algebras. Studien zur Algebra und ihre Anwendungen, Band 4. Akademic-Verlag, Berlin, 1978.

    MATH  Google Scholar 

  4. M.R. Vaughan-Lee. Varieties of Lie algebras. Q.J. Math., Oxf. II Ser., 21 (1970), 297–308.

    Article  MathSciNet  MATH  Google Scholar 

  5. V.S. Drenski. On identities in Lie algebras (in Russian). Algebra Logika 13(1974), 265–290. (English translation: Algebra Logic 13 (1974), 150–165 (1975)).

    Article  MathSciNet  Google Scholar 

  6. B.I. Plotkin. Varieties of group representations (in Russian). Usp. Mat. Nauk, 32 (1977), No. 5(197), 3–68. (English translation: Russ. Math. Surveys, 32 (1977), No. 5, 1–72).

    MathSciNet  MATH  Google Scholar 

  7. B.I. Plotkin. Varieties in representations of finite groups. Locally stable varieties. Matrix groups and varieties of representations (in Russian). Usp. Mat. Nauk, 34 (1979), No. 4(208), 65–95. (English translation: Russ. Math. Surveys, 34 (1979), No. 4, 69–103).

    MathSciNet  MATH  Google Scholar 

  8. A.Yu. Ol'Šanskii. On the problem of a finite basis of identities in groups (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 34 (1970), 376–384. (English translation: Math. USSR, Izv., 4 (1970), 381–389 (1971)).

    MathSciNet  Google Scholar 

  9. S.I. Adian. Infinite irreducible systems of group identities (in Russian). Dokl. Akad. Nauk SSSR, 190 (1970), 499–501. (English translation: Soviet Math., Dokl., 11 (1970), 113–115).

    MathSciNet  Google Scholar 

  10. M.R. Vaughan-Lee. Uncountably many varieties of groups. Bull. Lond. Math. Soc., 2 (1970), 280–286.

    Article  MathSciNet  MATH  Google Scholar 

  11. R.M. Bryant and M.F. Newman. Some finitely based varieties of groups. Proc. Lond. Math. Soc., III Ser., 28 (1974), 237–252.

    Article  MathSciNet  MATH  Google Scholar 

  12. Yu.N. Mal'cev. Basis for identities of the algebra of upper triangular matrices (in Russian). Algebra Logika, 10 (1971), 393–400. (English translation: Algebra Logic, 10 (1971), 242–247 (1973)).

    MathSciNet  Google Scholar 

  13. Yu.P. Razmyslov. The Jacobson radical in PI-algebras (in Russian). Algebra Logika, 13 (1974), 337–360. (English translation: Algebra Logic, 13 (1974), 192–204 (1975)).

    MathSciNet  Google Scholar 

  14. A.N. Krasil'nikov. The finite basis property for certain varieties of Lie algebras (in Russian). Vestn. Mosk. Univ., Ser. 1, No. 2 (1982), 34–38. (English translation: Mosc. Univ. Math. Bull., 37, No. 2 (1982), 44–48).

    MathSciNet  MATH  Google Scholar 

  15. D.E. Cohen. On the laws of a metabelian variety. J. Algebra 5 (1967), 267–273.

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Higman. Ordering by divisibility in abstract algebras. Proc. Lond. Math. Soc., III Ser., 2 (1952), 326–336.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Luchezar L. Avramov Kerope B. Tchakerian

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Krasil'nikov, A.N., Šmel'kin, A.L. (1988). On the laws of finite dimensional representations of solvable lie algebras and groups. In: Avramov, L.L., Tchakerian, K.B. (eds) Algebra Some Current Trends. Lecture Notes in Mathematics, vol 1352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082021

Download citation

  • DOI: https://doi.org/10.1007/BFb0082021

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50371-2

  • Online ISBN: 978-3-540-45994-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics