Quadratic Poisson brackets compatible with an algebra structure
classification
✦ hep-th
math.QA
keywords
bracketscompatiblemultiplicationpoissonquadraticalgebrabilinearbracket
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Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
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