4 papers
Trace radicals and cocenters of free products
Nikita Safonkin
We call a unital associative algebra trace residually finite-dimensional if its elements are separated by finite-dimensional representations and its cocenter is separ…
Double Transposed Poisson Algebras
Maxime Fairon, Nikita Safonkin
We introduce double transposed Poisson algebras, a noncommutative analogue of the transposed Poisson algebras of Bai, Bai, Guo and Wu that is compatible with the Kontsevich--Rosenb…
Coupled double Poisson brackets
Nikita Safonkin
We introduce coupled double Poisson brackets on an associative algebra as pairs consisting of a generalized Van den Bergh's double Poisson bracket and a generalized Fairon--McC…
What is a double star-product?
Nikita Safonkin
Double Poisson brackets, introduced by M. Van den Bergh in 2004, are noncommutative analogs of the usual Poisson brackets in the sense of the Kontsevich-Rosenberg principle: they i…