10 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…
Double Poisson brackets and involutive representation spaces
Grigori Olshanski, Nikita Safonkin
Let be an algebraically closed field of characteristic and be a finitely generated associative -algebra, in general noncommutative. One assigns to a sequ…
Remarks on Yangian-type algebras and double Poisson brackets
Grigori Olshanski, Nikita Safonkin
This short note is an announcement of results. We continue the study of Yangian-type algebras initiated in the paper arXiv:2208.04809. These algebras share a number of properties o…
Semifinite harmonic functions on the direct product of graded graphs
Pavel Nikitin, Nikita Safonkin
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite in…
Semifinite harmonic functions on the zigzag graph
Nikita Safonkin
We study semifinite harmonic functions on the zigzag graph, which corresponds to Pieri's rule for the fundamental quasisymmetric functions . The main problem, which we sol…
Semifinite harmonic functions on branching graphs
Nikita Safonkin
We study semifinite harmonic functions on arbitrary branching graphs. We give a detailed exposition of an algebraic method which allows one to classify semifinite indecomposable ha…
Semifinite harmonic functions on the Gnedin-Kingman graph
Nikita Safonkin
We study the Gnedin-Kingman graph, which corresponds to Pieri's rule for the monomial basis in the algebra of quasisymmetric functions. The paper contains…