Derived brackets for fat Leibniz algebras. (English) Zbl 1434.17004
Summary: We show that (1) the standard complex \(C(L)\) of a Leibniz algebra \(L\) can be defined analogously to that of a Courant algebroid and (2) the canonical 3-cocycle in \(C(L)\) defined in the case of a Courant algebroid admits a generalization to the case of a Leibniz algebra, which turns out to be a coboundary. We consider a subcomplex consisting of “representable cochains” and endow it with a bracket making it a \((- 2)\)-shifted Poisson algebra. Finally, we show that the Leibniz bracket of a fat Leibniz algebra can be described as a derived bracket.
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