Reference : Study of formality for the Heisenberg algebra
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Physical, chemical, mathematical & earth Sciences : Mathematics
Study of formality for the Heisenberg algebra
Elchinger, Olivier mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] Heisenberg Lie algebra ; Chevalley-Eilenberg cohomology ; formality equations
[en] In this paper, we compute the Chevalley-Eilenberg cohomology of the three-dimensional Heisenberg Lie algebra with values in its universal enveloping algebra. We also compute the Schouten brackets on cochains and cohomology level in order to write the formality equations. It turns out that there is no formality, and that the perturbed L∞ structure on the cohomology has non-trivial terms in infinitely many degrees.

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