Advertisement

Communications in Mathematical Physics

, Volume 154, Issue 3, pp 555–568 | Cite as

Representations of central extensions of differentiably simple lie superalgebras

  • Shun-Jen Cheng
Article

Abstract

LetS be a simple Lie algebra of characteristic 0 and Λ(n) be the Grassmann superalgebra inn indeterminates. We can form the Lie superalgebraS ⊗ Λ(n). The purpose of this paper is to classify all finite dimensional irreducible representations of all central extensions ofS ⊗ Λ(n). We will also give a character formula for these representations.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Irreducible Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B] Block, R.E.: Determination of differentiably simple rings with a minimal ideal. Ann. Math.90, 2, 433–459 (1969)Google Scholar
  2. [C] Cheng, S.-J.: Differentiably simple Lie superalgebras. Dissertation, Harvard Univ. (1993)Google Scholar
  3. [K1] Kač, V.G.: Lie superalgebras. Adv. in Math.26 (1977)Google Scholar
  4. [K2] Kač, V.G.: Infinite dimensional Lie algebras. (3rd ed.) Cambridge: Cambridge University Press 1990Google Scholar
  5. [K3] Kač, V.G., Todorov, I.T.: Superconformal current algebras and their representations. Comm. Math. Phys.102, 337–347 (1985)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Shun-Jen Cheng
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeU.S.A.

Personalised recommendations