Reynolds operator on functors |
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Authors: | Amelia Álvarez Carlos Sancho |
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Institution: | a Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06006 Badajoz, Spainb Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain |
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Abstract: | Let be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗=R×B∗ as R-algebras and the first projection A∗→R is the unit of A. If M is a dual functor of G-modules and wG?(1,0)∈R×B∗=A∗, we prove that MG=wG⋅M and M=wG⋅M⊕(1−wG)⋅M; hence, the Reynolds operator can be defined on M. |
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Keywords: | Primary 14L24 Secondary 14L17 |
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