Skip to main content
SpringerLink
Log in

On the Cohomology for the Witt Algebra W(1,1)

  • Chapter
Non-Associative Algebra and Its Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 303))

Abstract

In this paper the cohomology ring for the restricted enveloping algebra of W(1,1) is computed. The procedure given depends on calculating the ordinary Lie algebra cohomology of a certain p-unipotent subalgebra of W(1,1). For low primes this computation becomes tractable and formulas for the dimensions of the graded components of the cohomology ring are given.

supported by NSF grant. DMS-9206284

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. H. Andersen, J. C. Jantzen, Cohomology of induced representations for algebraic groups, Math. Ann. 269 (1984), 487–525.

    MathSciNet  MATH  Google Scholar 

  2. R. E. Block, R. L. Wilson, Classification of restricted simple Lie algebras, J. Algebra 114 (1988), 115–259.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. M. Friedlander, B. J. Parshall, Cohomology of Lie algebras and algebraic groups, Amer..1. Math. 108 (1986), 225–253.

    MathSciNet  Google Scholar 

  4. E. M. Friedlander, B. J. Parshall, Support varieties for restricted Lie algebras, Invent. Math. 86 (1986), 553–562.

    Article  MathSciNet  MATH  Google Scholar 

  5. E. M. Friedlander, B. J. Parshall, Geometry of p-unipotent Lie algebras, J. Algebra 109 (1987), 25–45.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. R. Holmes, D. K. Nakano, Block degeneracy and Cartan invariants for graded Lie algebras of Cartan type, J. Algebra 161 (1993), 155–170.

    Article  MathSciNet  MATH  Google Scholar 

  7. Z. Lin, D. K. Nakano, Algebraic group techniques in the representation and cohomology theory of Lie algebras of Cartan type, preprint.

    Google Scholar 

  8. Z. Lin, D. K. Nakano, Modular representation theory for Lie algebras of Cartan type, preprint.

    Google Scholar 

  9. D. K. Nakano, Projective modules over Lie algebras of Cartan type, Memoirs of AMS 98 (470) (1992).

    Google Scholar 

  10. R. L. Wilson, Automorphisms of graded Lie algebras of Cartan type, Comm. Alg. 3 (7) (1975), 591–613.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Northwestern University, Evanston, Illinois, 60208, USA

    Daniel K. Nakano

Authors
  1. Daniel K. Nakano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Santos González

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Nakano, D.K. (1994). On the Cohomology for the Witt Algebra W(1,1). In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_48

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0990-1_48

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4429-5

  • Online ISBN: 978-94-011-0990-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation