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Calculations on Lie Algebra of the Group of Affine Symplectomorphisms
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-01-23
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Altawallbeh, Zuhier. 2017. Calculations on Lie Algebra of the Group of Affine Symplectomorphisms. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-5.
https://search.emarefa.net/detail/BIM-1123349
Modern Language Association (MLA)
Altawallbeh, Zuhier. Calculations on Lie Algebra of the Group of Affine Symplectomorphisms. Advances in Mathematical Physics No. 2017 (2017), pp.1-5.
https://search.emarefa.net/detail/BIM-1123349
American Medical Association (AMA)
Altawallbeh, Zuhier. Calculations on Lie Algebra of the Group of Affine Symplectomorphisms. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-5.
https://search.emarefa.net/detail/BIM-1123349
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123349