119 citations · 638 across the 44 of their papers we have counts for
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Calculating Galois groups of third order linear differential equations with parameters
Andrei Minchenko, Alexey Ovchinnikov
Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a pa…
Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer
We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives i…
Extensions of differential representations of SL(2) and tori
Andrey Minchenko, Alexey Ovchinnikov
Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which…
Zariski Closures of Reductive Linear Differential Algebraic Groups
Andrey Minchenko, Alexey Ovchinnikov
Linear differential algebraic groups (LDAGs) appear as Galois groups of systems of linear differential and difference equations with parameters. These groups measure differential-a…
Differential Tannakian Categories
Alexey Ovchinnikov
We define a differential Tannakian category and show that under a natural assumption it has a fibre functor. If in addition this category is neutral, that is, the target category f…
Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations
Alexey Ovchinnikov
We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion…
Tannakian approach to linear differential algebraic groups
Alexey Ovchinnikov
Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear di…