On dynamical finiteness properties of algebraic group shifts

2020/10/08 by Xuan Kien Phung, Phung, Xuan Kien · 1 citation
Computer Science · Engineering · #Algebraic Geometry (math.AG) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2010.04035

openalex publication_date 2020/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group and let V be an algebraic group over an algebraically closed field. We introduce algebraic group subshifts Σ⊂ V^G which generalize both the class of algebraic sofic subshifts of V^G and the class of closed group subshifts over finite group alphabets. When G is a polycyclic-by-finite group, we show that V^G satisfies the descending chain condition and that the notion of algebraic group subshifts, the notion of algebraic group sofic subshifts, and that of algebraic group subshifts of finite type are all equivalent. Thus, we obtain extensions of well-known results of Kitchens and Schmidt to cover the case of many non-compact group alphabets.

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