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In this paper, we follow and extend a group-theoretic method introduced by Greenleaf-Iosevich-Liu-Palsson (GILP) to study finite points configurations spanned by Borel sets in \mathbb{R}^n,n\geq 2,n\in\mathbb{N}.We remove a technical continuity condition in a GILP's theorem in [GILP15]. This allows us to extend the Wolff-Erdogan dimension bound for distance sets to finite points configurations with kpoints for k\in\{2,\dots,n+1\}.At the end of this paper, we extend this group-theoretic ...

REAL HYPERSURFACES IN COMPLEX SPACE FORMS ATTAINING EQUALITY IN AN INEQUALITY INVOLVING A CONTACT δ-INVARIANT

Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum linear space to be (semi)prime. These are then used to determine (semi)primeness of certain smash products with quantum affine spaces. This extends Bergen's work on Taft algebras.

We consider frieze sequences corresponding to sequences of cluster mutations for affine D and E type quivers. We show that the cluster variables satisfy linear recurrences with periodic coefficients, which imply the constant coefficient relations found by Keller and Scherotzke. Viewing the frieze sequence as a discrete dynamical system, we reduce it to a symplectic map on a lower dimensional space and prove Liouville integrability of the latter.

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