2019
Том 71
№ 10

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On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers

Tushev A. V.

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Abstract

In this paper, we prove the existence of an elementα of the group algebra $A=ℂF$ of a free group $F$ with two generatorsx andy over the field of complex numbers $C$ such that, for any complex $a$ and $b$ for which $¦a¦=¦b¦=1$, we have $A ∩ ϑ_{a,b} (α)A=0$, where $ϑ_{a,b}$ ($α$ is an automorphism of $A$ that maps $x,y$ into $a_x, b_y$, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.”

English version (Springer): Ukrainian Mathematical Journal 47 (1995), no. 4, pp 663–664.

Citation Example: Tushev A. V. On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers // Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 571-572.

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