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Matematicheskie Zametki, 2007, Volume 82, Issue 6, Pages 811–821
DOI: https://doi.org/10.4213/mzm4182 (Mi mzm4182) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Tensor Products of Algebras and Their Applications to the Construction of Anosov Diffeomorphisms

V. V. Gorbatsevich

Moscow State Aviation Technological University
Full-text PDF (456 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4182
Abstract: In this paper, we develop algebraic approaches to the construction of Anosov diffeomorphisms on compact manifolds. Two mutually dual constructions are described, which provide numerous new examples of Anosov diffeomorphisms on nilmanifolds. The basis of the constructions is the operation of tensor multiplication of Lie algebras by appropriate finite-dimensional associative-commutative algebras. Several examples illustrating the general method are given.
Keywords: Anosov diffeomorphism, nilpotent Lie group, hyperbolic nilpotent Lie group, nilmanifold, associative-commutative algebra.
Received: 13.09.2006
English version:
Mathematical Notes, 2007, Volume 82, Issue 6, Pages 733–740
DOI: https://doi.org/10.1134/S000143460711017X
Bibliographic databases:
UDC: 519.46
Language: Russian
Citation: V. V. Gorbatsevich, “Tensor Products of Algebras and Their Applications to the Construction of Anosov Diffeomorphisms”, Mat. Zametki, 82:6 (2007), 811–821; Math. Notes, 82:6 (2007), 733–740
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    1. V. V. Gorbatsevich, “Foundations of Lie theory for EE-structures and some of its applications”, Izv. Math., 86:2 (2022), 252–274  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Dekimpe K., Verheyen K., “Anosov diffeomorphisms on nilmanifolds modelled on a free nilpotent Lie group”, Dyn. Syst., 24:1 (2009), 117–121  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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