Abstract
Let \(\mathfrak{A}_n\) be the set of all those vectors of the standard lattice ℤn whose coordinates are pairwise incomparable modulo n. In this paper, we analyze the group structure on \(\mathfrak{A}_n\) that arises from the construction of a deformation of multiplication described by V.M. Buchstaber. We present a geometric realization of this group in the ambient space ℝn ⊃ ℤn and find its generators and relations.
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V. M. Buchstaber, “Semigroups of maps into groups, operator doubles, and complex cobordisms,” in Topics in Topology and Mathematical Physics (Am. Math. Soc., Providence, RI, 1995), AMS Transl., Ser. 2, 170, pp. 9–31.
C. Kassel, Quantum Groups (Springer, New York, 1995; Phasis, Moscow, 1999).
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups (Springer, Berlin, 1972; Nauka, Moscow, 1980).
W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations (Dover, New York, 1966; Nauka, Moscow, 1974).
A. P. Poyarkov and A. I. Garber, “Permutable polyhedra,” Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 2, 3–8 (2006) [Mosc. Univ. Math. Bull. 61 (2), 1–6 (2006)].
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Original Russian Text © S.Yu. Tsarev, 2014, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 286, pp. 231–240.
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Tsarev, S.Y. Geometric aspects of a deformation of the standard addition on integer lattices. Proc. Steklov Inst. Math. 286, 209–218 (2014). https://doi.org/10.1134/S008154381406011X
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DOI: https://doi.org/10.1134/S008154381406011X