Calculations on Lie Algebra of the Group of Affine Symplectomorphisms

Zuhier Altawallbeh
2017 Advances in Mathematical Physics  
We find the image of the affine symplectic Lie algebra gn from the Leibniz homology HL⁎(gn) to the Lie algebra homology H⁎Lie(gn). The result shows that the image is the exterior algebra ∧⁎(wn) generated by the forms wn=∑i=1n(∂/∂xi∧∂/∂yi). 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
more » ... omology HH⁎-1(U(gn)) is isomorphic to H⁎-1Lie(gn,U(gn)ad). Explicitly, we use the alternation of multilinear map, in our elements, to do certain calculations.
doi:10.1155/2017/9513237 fatcat:grncauzbxnbprhfrxguy7g2fby