Institute for Mathematical Physics on the Entropy Theory of Finitely Generated Nilpotent Group Actions on the Entropy Theory of Finitely Generated Nilpotent Group Actions

Let G be a finitely generated nilpotent torsionfree group. The entropy theory for G-actions is investigated. The Pinsker algebra of such actions is described explicitly. The comlpetley positive systems are shown to have a sort of 'asypmtotic independence prop-erty', just as in the case of Z d-actions. A notion of K-system for G-actions is considered. The properties of invariant partitions are used to prove that the property of complete positivity is equivalent to the properties of K-system and K-mixing. The relationship between the K-systems and some spectral and mixing properties of G-actions is clarified.