The solution to the embedding problem of a (differential) Lie algebra into its Wronskian envelope |
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Authors: | Laurent Poinsot |
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Affiliation: | 1. LIPN - UMR CNRS 7030, University Paris 13, Sorbonne Paris Cité, Villetaneuse, France;2. CReA, French Air Force Academy, Base aérienne 701, Salon-de-Provence, France |
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Abstract: | Any commutative algebra equipped with a derivation may be turned into a Lie algebra under the Wronskian bracket. This provides an entirely new sort of a universal envelope for a Lie algebra, the Wronskian envelope. The main result of this paper is the characterization of those Lie algebras which embed into their Wronskian envelope as Lie algebras of vector fields on a line. As a consequence we show that, in contrast to the classical situation, free Lie algebras almost never embed into their Wronskian envelope. |
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Keywords: | Differential algebra universal envelope vector fields Wronskian bracket |
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