Low Dimensional Homology Groups of the Orthosymplectic Lie Superalgebra $\osp(1,2)$

Authors

  • Guy Roger Biyogmam Southwestern Oklahoma State university

Keywords:

Lie superalgebras, Homology of Lie superalgebras.

Abstract

We realize the Lie superalgebra $\osp(1,2)$ in terms of first order differential operators and endow it with the Lie superbracket of vector fields to determine the basis (co)cycles of low dimensional (co)homology groups of $\osp(1,2)$ with trivial coefficients, using the complex introduced by Tanaka \cite{T}. Our calculations agree with the result obtained by Fuks and Leites.

Downloads

Published

2014-11-04

Issue

Vol. 7 No. 4: (October 2014)

Section

Algebra

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Low Dimensional Homology Groups of the Orthosymplectic Lie Superalgebra $\osp(1,2)$. (2014). European Journal of Pure and Applied Mathematics, 7(4), 395-404. https://www.ejpam.com/index.php/ejpam/article/view/1881