4 problems

Let $S({\bf C}^{N})^{\infty}_{\mathrm{AP}}$ denote the asymptotically periodic sequences and let $S({\bf C}^{N})^{\infty}_{\mathrm{EP}}$ denote the eventually periodic sequences. W…

Let $n\geq 2$, and let $u\in S([n]^2)$ be the product of transpositions determined by four distinct pairs $(a_1,b_1),(a_1,b_2),(a_2,b_3),(a_2,b_4)\in[n]^2$, where $a_1\ne a_2$. For…

Let $S$ be the right LCM semigroup under consideration, let $\mathcal{P}$ be its family of primes, let $\mathcal{A}(S)$ be the subalgebra of $\mathcal{Q}(S)$ generated by…

Let ${\mathcal O}_n$ be a Cuntz algebra, let $\lambda$ be an endomorphism associated to an induced permutation, and let $\alpha$ be a Bogolyubov automorphism of ${\mathcal O}_n$. E…