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Czechoslovak Journal of Physics

, Volume 54, Issue 11, pp 1159–1164 | Cite as

Casimir Elements for Some Graded Lie Algebras and Superalgebras

  • Yuri Bahturin
  • Alexander Molev
Article

Abstract

We consider a class of Lie algebras L such that L admits a grading by a finite Abelian group so that each nontrivial homogeneous component is one-dimensional. In particular, this class contains simple Lie algebras of types A, C and D where in C and D cases the rank of L is a power of 2. We give a simple construction of a family of central elements of the universal enveloping algebra U(L). We show that for the A-type Lie algebras the elements coincide with the Gelfand invariants and thus generate the center of U(L). The construction can be extended to Lie superalgebras with the additional assumption that the group grading is compatible with the parity grading.

Keywords

graded Lie algebra Casimir element 

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Copyright information

© Institute of Physics, Academy of Sciences of Czech Republic 2004

Authors and Affiliations

  • Yuri Bahturin
    • 1
  • Alexander Molev
    • 2
  1. 1.Department of Mathematics and Statistics
  2. 2.School of Mathematics and Statistics

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