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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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REPRESENTATION VARIETY OF BAUMSLAG-SOLITAR GROUPS IN THE CASE OF NOT COPRIME EXPONENTS

Abstract

Representation varieties of Baumslag – Solitar groups BS (p, q) are investigated in the case when p and q are not coprime. Irreducible components of these varieties are found, their dimensions are calculated and their rationality is proved.

About the Authors

V. V. Beniash-Kryvets
Belarusian State University, Minsk
Belarus


I. O. Govorushko
Belarusian State Pedagogikal University named after M. Tank, Minsk
Belarus


References

1. Lubotzky, A. Varieties of representations of finitely generated groups / A. Lubotzky, A. Magid // Memoirs AMS. – 1985. – Vol. 58, N 336. – P. 1–116.

2. Baumslag, G. Some two-generator one-relator non-hopfian groups / G. Baumslag, D. Solitar // Bull. AMS. – 1962. – Vol. 68, N 3. – P. 199–201.

3. Беняш-Кривец, В. В. О многообразиях представлений групп Баумслага – Солитера / В. В. Беняш-Кривец, И. О. Говорушко // Вестн. Белорус. гос. ун-та. Сер. 1, Физика. Математика. Информатика. – 2014. –№ 2. –С. 43–45.

4. Шафаревич, И. Р. Основы алгебраической геометрии: в 2 т. / И. Р. Шафаревич. – М.: Наука, 1988. – Т. 1.


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ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)