Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2017, Article ID 9513237, 5 pages
https://doi.org/10.1155/2017/9513237
Research Article

Calculations on Lie Algebra of the Group of Affine Symplectomorphisms

Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan

Correspondence should be addressed to Zuhier Altawallbeh; moc.liamg@0891reihuz

Received 13 November 2016; Accepted 4 January 2017; Published 23 January 2017

Academic Editor: Manuel De León

Copyright © 2017 Zuhier Altawallbeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We find the image of the affine symplectic Lie algebra from the Leibniz homology to the Lie algebra homology . The result shows that the image is the exterior algebra generated by the forms . Given the relevance of Hochschild homology to string topology and to get more interesting applications, we show that such a map is of potential interest in string topology and homological algebra by taking into account that the Hochschild homology is isomorphic to . Explicitly, we use the alternation of multilinear map, in our elements, to do certain calculations.