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…
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 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…