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An étale module for a linear algebraic group G is a complex vector space V with a rational G-action on V that has a Zariski-open orbit and dim G = dim V . Such a module is called super-étale if the stabilizer of a point in the open orbit is trivial. Popov (2013) proved that reductive algebraic groups admitting super-étale modules are special algebraic groups. He further conjectured that a reductive...
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized and differential Galois theories. To achieve this, we expand the representation theory of linear differential algebraic groups and develop new algorithms that calculate unipotent radicals of parameterized differential Galois groups...
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