24 citations · 69 across the 20 of their papers we have counts for
22 papers
Relations between categorifications of higher-dimensional type cluster combinatorics
Mikhail Gorsky, Nicholas J. Williams
We consider three categories arising from the higher Auslander algebras of type in relation to -dimensional cluster combinatorics: -exact subcategory of the module catego…
A Categorification of Subword Complexes and Its Hall Algebra
Mikhail Gorsky, Zijun Li
Bergeron and Ceballos defined a Hopf algebra structure on equivalence classes of subword complexes. We introduce a category of subword complexes, endow it with a proto-exact-like s…
Counting in Calabi--Yau categories, with applications to Hall algebras and knot polynomials
Mikhail Gorsky, Fabian Haiden
We show that homotopy cardinality -- a priori ill-defined for many dg-categories, including all periodic ones -- has a reasonable definition for even-dimensional Calabi--Yau (evenC…
Cluster algebras in Lie and Knot theory
Mikhail Gorsky, José Simental
This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.
Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
Xin Fang, Mikhail Gorsky, Yann Palu +2
We extend results of Brüstle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpre…
Hereditary extriangulated categories: Silting objects, mutation, negative extensions
Mikhail Gorsky, Hiroyuki Nakaoka, Yann Palu
In this article, we initiate the study of hereditary extriangulated categories. Many important categories arising in representation theory in connection with various theories of mu…
A structural view of maximal green sequences
Mikhail Gorsky, Nicholas J. Williams
We study the structure of the set of all maximal green sequences of a finite-dimensional algebra. There is a natural equivalence relation on this set, which we show can be interpre…
A functorial approach to rank functions on triangulated categories
Teresa Conde, Mikhail Gorsky, Frederik Marks +1
We study rank functions on a triangulated category via its abelianisation . We prove that every rank function on can be i…
Cluster structures on braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +3
We show the existence of cluster -structures and cluster Poisson structures on any braid variety, for any simple Lie group. The construction is achieved via weave calc…
Positroid Links and Braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
We study braid varieties and their relation to open positroid varieties. We discuss four different types of braids associated to open positroid strata and show that their associate…
Positive and negative extensions in extriangulated categories
Mikhail Gorsky, Hiroyuki Nakaoka, Yann Palu
We initiate the study of derived functors in the setting of extriangulated categories. By using coends, we adapt Yoneda's theory of higher extensions to this framework. We show tha…
Algebraic Weaves and Braid Varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain t…
Subword complexes and 2-truncated cubes
Mikhail Gorsky
For a Coxeter element of a finite Coxeter group, we consider a family of subword complexes parameterized by reduced expressions of the longest element. This family generalizes…
On the lattices of exact and weakly exact structures
Rose-Line Baillargeon, Thomas Brüstle, Mikhail Gorsky +1
We initiate in this article the study of weakly exact structures, a generalization of Quillen exact structures. We introduce weak counterparts of one-sided exact structures and sho…
Exact structures and degeneration of Hall algebras
Xin Fang, Mikhail Gorsky
We study degenerations of the Hall algebras of exact categories induced by degree functions on the set of isomorphism classes of indecomposable objects. We prove that each such deg…
Semi-derived and derived Hall algebras for stable categories
Mikhail Gorsky
Given a Frobenius category satisfying certain finiteness conditions, we consider the localization of its Hall algebra at the classes of all projectiv…
Subword complexes and nil-Hecke moves
Mikhail Gorsky
For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρis a group element.…
Subword complexes and edge subdivisions
Mikhail Gorsky
For a finite Coxeter group, a subword complex is a simplicial complex associated with a pair (Q, π), where Q is a word in the alphabet of simple reflections, is a group element…
Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras
Mikhail Gorsky
Inspired by recent work of Bridgeland, from the category C^b(E) of bounded complexes over an exact category E satisfying certain finiteness conditions, we construct an associative…
A braid group action on parking functions
Evgeny Gorsky, Mikhail Gorsky
We construct an action of the braid group on strands on the set of parking functions of cars such that elementary braids have orbits of length 2 or 3. The construction is m…
On Young diagrams, flips and cluster algebras of type A
Mikhail Gorsky
We give a new simple description of the canonical bijection between the set of triangulations of n-gon and some set of Young diagrams. Using this description, we find flip transfor…
Proof of Gal's conjecture for the D series of generalized associahedra
Mikhail Gorsky
In this short note we consider generalized associahedra of type D_n. We prove that these simple flag polytopes are not nestohedra for n > 3, but the statement of Gal's conjecture h…