101 citations · 968 across the 80 of their papers we have counts for
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math.QA2006
An operadic approach to deformation quantization of compatible Poisson brackets
Vladimir Dotsenko
We construct an analogue of the Livernet--Loday operad for two compatible brackets. The Livernet--Loday operad can be used to define -products and deformation quantization f…
math.RA2006★ 19 cited
Quadratic algebras related to the bihamiltonian operad
Mikhail Bershtein, Vladimir Dotsenko, Anton Khoroshkin
We prove the conjectures on dimensions and characters of some quadratic algebras stated by BLFeigin. It turns out that these algebras are naturally isomorphic to the duals of…
math.QA2006★ 66 cited
Character formulas for the operad of two compatible brackets and for the bihamiltonian operad
Vladimir Dotsenko, Anton Khoroshkin
We compute dimensions of the components for the operad of two compatible brackets and for the bihamiltonian operad. We also obtain character formulas for the representations of the…