On representation varie ties of some HNN-extensions of free groups

Authors

  • Alexandra N. Admiralova Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Valery V. Beniash-Kryvets Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk, Belarus

Keywords:

a group presentation, a representation variety, a dimension of a variety, a rational variety

Abstract

In the article we provide the description of the structure and the properties of representation varieties Rn(G(p,q)) of the groups with the presentation G(p,q) = ‹x1,…, x2, t|t(x12…xg2)q›, where g ≥ 3, |p| > q ≥ 1. Irreducible components of Rn(G(p,q)) are found, their dimensions are calculated and it is proved, that every irreducible component of Rn(G(p,q)) is a rational variety.

Author Biographies

  • Alexandra N. Admiralova, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

    postgraduate student at the department of higher algebra and information security, faculty of mathematics and mechanics

  • Valery V. Beniash-Kryvets, Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk, Belarus

    doctor of science (physics and mathematics), full professor; head of the department of higher algebra and information security, faculty of mathematics and mechanics

References

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  4. Benyash-Krivets VV, Govorushko IO. Representation and character varieties of the Baumslag – Solitar groups. Trudy Matematicheskogo instituta im. V. A. Steklova RAN. 2016;292:26 – 42. Russian. DOI: 10.1134/S0371968516010039.
  5. Benyash-Krivets VV, Govorushko IO. Mnogoobraziya predstavlenii grupp Baumslaga – Solitera v sluchae ne vzaimno prostykh pokazatelei [On representation varieties of Baumslag – Solitar groups in the case of not-coprime powers]. Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series. 2016;1:52–56. Russian.
  6. Admiralova AN, Beniash-Krivets VV. On representations varieties and characters of one class groups with one relation. Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika. 2016;3:166–172. Russian.
  7. Benyash-Krivets VV. Representation varieties of non-Euclidean crystallographic groups. Doklady NAN Belarusi. 2000;44(4): 37– 40. Russian.
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Published

2019-01-19

Issue

No. 2 (2018): Journal of the Belarusian State University. Mathematics and Informatics

Section

Geometry and Algebra

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How to Cite

[1]
Admiralova, A.N. and Beniash-Kryvets, V.V. 2019. On representation varie ties of some HNN-extensions of free groups. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Jan. 2019), 10–16.