On a homotopy version of the Duflo isomorphism
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2020-03
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Journal Article
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no
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Abstract
For a finite-dimensional Lie algebra g, the Duflo map Sg→Ug defines an isomorphism of g-modules. On g-invariant elements, it gives an isomorphism of algebras. Moreover, it induces an isomorphism of algebras on the level of Lie algebra cohomology H(g,Sg)→H(g,Ug). However, as shown by J. Alm and S. Merkulov, it cannot be extended in a universal way to an A∞-isomorphism between the corresponding Chevalley–Eilenberg complexes. In this paper, we give an elementary and self-contained proof of this fact using a version of M. Kontsevich’s graph complex.
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published
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110 (3)
Pages / Article No.
423 - 444
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Springer
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Subject
Duflo isomorphism; Graph complexes; Operads
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03521 - Axhausen, Kay W. (emeritus) / Axhausen, Kay W. (emeritus)
02655 - Netzwerk Stadt u. Landschaft ARCH u BAUG / Network City and Landscape ARCH and BAUG