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

  • A. V. Tushev

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.”
Published
25.04.1995
How to Cite
TushevA. V. “On Ideals of the Group Algebra of a Free Group of Degree of Freedom Two over the Field of Complex Numbers”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 47, no. 4, Apr. 1995, pp. 571-2, https://umj.imath.kiev.ua/index.php/umj/article/view/5460.
Section
Short communications