Displaying similar documents to “Affin manifolds with nilpotent holonomy.”

On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus

Rafał Pikuła (2010)

Studia Mathematica

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Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. We show that the enveloping semigroup E(X,G) of the dynamical system (X,G) is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of E(X,G) as a quotient space.