Dmitriy Voloshyn

activity

20212025

most citedMultiple generalized cluster structures on

D (GL_{n})

2 citations · 2 across the 4 of their papers we have counts for

collaborators

4 papers

math.RT2025

Multiple rational normal forms in Lie theory

Dmitriy Voloshyn

We study the decomposition of a generic element $g \in G$ of a connected reductive complex algebraic group $G$ in the form $g = N (g) B (g) u ˉ N (g)^{- 1}$ where $N: G \dashrighta…

math.QA2023

Generalized cluster structures related to Poisson duals of $SL_{n}$

Michael Gekhtman, Dmitriy Voloshyn

We study Poisson varieties $(SL_{n}, π_{Γ ˉ}^{†})$ parameterized by Belavin--Drinfeld quadruples $Γ ˉ := (Γ, r_{0})$ of type $A_{n - 1}$ along wit…

math.RT2023

Starfish lemma via birational quasi-isomorphisms

Dmitriy Voloshyn

We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows o…

math.RT2021★ 2 cited

Multiple generalized cluster structures on $D (GL_{n})$

Dmitriy Voloshyn

We produce a large class of generalized cluster structures on the Drinfeld double of $GL_{n}$ that are compatible with Poisson brackets given by Belavin-Drinfeld classificatio…

Multiple rational normal forms in Lie theory

Generalized cluster structures related to Poisson duals of SLn​

Starfish lemma via birational quasi-isomorphisms

Multiple generalized cluster structures on D(GLn​)

Generalized cluster structures related to Poisson duals of $SL_{n}$

Multiple generalized cluster structures on $D (GL_{n})$