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Calculations on Lie Algebra of the Group of Affine Symplectomorphisms

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  • Zuhier Altawallbeh

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.

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  • Zuhier Altawallbeh, 2017. "Calculations on Lie Algebra of the Group of Affine Symplectomorphisms," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-5, January.
    • Handle: RePEc:hin:jnlamp:9513237
    DOI: 10.1155/2017/9513237
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