4 papers · 1 filter
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…
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…
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…