Calculations on Lie Algebra of the Group of Affine Symplectomorphisms
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 topolog...
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| Format: | Article |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9513237 |
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| author | Zuhier Altawallbeh |
| author_facet | Zuhier Altawallbeh |
| author_sort | Zuhier Altawallbeh |
| collection | DOAJ |
| description | 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 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. |
| format | Article |
| id | doaj-art-0d6eb4d71a0047b4b9251a587772a5c6 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0d6eb4d71a0047b4b9251a587772a5c62025-02-03T05:52:52ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/95132379513237Calculations on Lie Algebra of the Group of Affine SymplectomorphismsZuhier Altawallbeh0Department of Mathematics, Tafila Technical University, Tafila 66110, JordanWe 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 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.http://dx.doi.org/10.1155/2017/9513237 |
| spellingShingle | Zuhier Altawallbeh Calculations on Lie Algebra of the Group of Affine Symplectomorphisms Advances in Mathematical Physics |
| title | Calculations on Lie Algebra of the Group of Affine Symplectomorphisms |
| title_full | Calculations on Lie Algebra of the Group of Affine Symplectomorphisms |
| title_fullStr | Calculations on Lie Algebra of the Group of Affine Symplectomorphisms |
| title_full_unstemmed | Calculations on Lie Algebra of the Group of Affine Symplectomorphisms |
| title_short | Calculations on Lie Algebra of the Group of Affine Symplectomorphisms |
| title_sort | calculations on lie algebra of the group of affine symplectomorphisms |
| url | http://dx.doi.org/10.1155/2017/9513237 |
| work_keys_str_mv | AT zuhieraltawallbeh calculationsonliealgebraofthegroupofaffinesymplectomorphisms |