6 problems

Cyclic cohomology conjecture. The cyclic cohomology of $A^{\infty}$ is given by

Let $A^{\infty}$ be the smooth subalgebra of the group $C^*$-algebra associated with the dihedral group, and let $HC^n(A^{\infty})$ denote its cyclic cohomology in degree $n$. Cycl…

Let $G$) be an exponential solvable Lie group, and let ${\mathcal J}_1\subseteq{\mathcal J}_2$ be closed two-sided ideals of $C^*(G)$ such that ${\mathcal J}_2/{\mathcal J}_1$ is a…

Let $C^*(\mathbb{Z}[1/6])$ be regarded as a subalgebra of $C^*(\mathfrak{F}_{2,3})$, let $\operatorname{TSt}(C^*(\mathfrak{F}_{2,3}))$ denote the tracial states, call a state condi…

Real-rank-zero conjecture. Then $G$ is locally finite.

Kadison–Kaplansky conjecture. The algebra $C^*_r\Gamma$ contains no non-trivial projections. The conjecture is presented as a consequence of surjectivity of the Baum–Connes assembl…