2019
Том 71
№ 10

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

Tushev A. V.

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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