20 citations · 84 across the 22 of their papers we have counts for
8 papers · 1 filter
A quantum anchor for higher Koszul brackets
Ekaterina Shemyakova, Yagmur Yilmaz
It is well known that the chain map between the de Rham and Poisson complexes on a Poisson manifold also maps the Koszul bracket of differential forms into the Schouten bracket of…
On super cluster algebras based on super Plücker and super Ptolemy relations
Ekaterina Shemyakova
We study super cluster algebra structure arising in examples provided by super Plücker and super Ptolemy relations. We develop the super cluster structure of the super Grassmannian…
Laplace invariants of differential operators
David Hobby, Ekaterina Shemyakova
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do tha…
Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator
Ekaterina Shemyakova, Theodore Voronov
We consider factorization problem for differential operators on the commutative algebra of densities (defined either algebraically or in terms of an auxiliary extended manifold) in…
Darboux transformations for differential operators on the superline
Sean Hill, Ekaterina Shemyakova, Theodore Voronov
We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation…
Orbits of Darboux groupoid for hyperbolic operators of order three
Ekaterina Shemyakova
Darboux transformations are viewed as morphisms in a Darboux category. Darboux transformations of type I which we defined previously, make an important subgroupoid consists of Darb…