Existence and equivalence of twisted products on a symplectic manifold |
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Authors: | André Lichnerowicz |
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Institution: | (1) Physique-Mathématique, College de France, 75 Paris Cedex, France |
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Abstract: | The twisted products play an important role in Quantum Mechanics 1, 2]. We introduce here a distinction between Vey *ν-products and strong Vey *ν-products and prove that each *ν-product is equivalent to a Vey *ν-product. If b
3(W)=0, the symplectic manifold (W, F) admits strong Vey *ν-products. If b
2(W)=0, all *ν-products are equivalent as well as the Vey Lie algebras. In the general case, we characterize the formal Lie algebras which
are generated by a *ν-product and we prove that the existence of a *ν-product is equivalent to the existence of a formal Lie algebra infinitesimally equivalent to a Vey Lie algebra at the first
order. |
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Keywords: | |
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