Email this article Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph
- Authors: Vershik A.M.1,2,3, Zatitskiy P.B.1,2
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics
- St. Petersburg State University
- Institute for Information Transmission Problems
- Issue: Vol 52, No 4 (2018)
- Pages: 258-269
- Section: Article
- URL: https://journals.rcsi.science/0016-2663/article/view/234538
- DOI: https://doi.org/10.1007/s10688-018-0236-1
- ID: 234538
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Abstract
We suggest a combinatorial classification of metric filtrations of measure spaces; a complete invariant of such a filtration is its combinatorial scheme, a measure on the space of hierarchies of the group Z. In turn, the notion of a combinatorial scheme is a source of new metric invariants of automorphisms approximated by means of basic filtrations. We construct a universal graph with an adic structure such that every automorphism can be realized on its path space.
About the authors
A. M. Vershik
St. Petersburg Department of Steklov Institute of Mathematics; St. Petersburg State University; Institute for Information Transmission Problems
Author for correspondence.
Email: avershik@gmail.com
Russian Federation, St. Petersburg; St. Petersburg; Moscow
P. B. Zatitskiy
St. Petersburg Department of Steklov Institute of Mathematics; St. Petersburg State University
Email: avershik@gmail.com
Russian Federation, St. Petersburg; St. Petersburg
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