AUTOMORPHISMS OF ENDOMORPHISM MONOIDS OF RELATIVELY FREE BANDS

Abstract

AbstractFor a set $X$ and a variety $\mathcal{V}$ of bands, let $B_{\mathcal{V}}(X)$ be the relatively free band in $\mathcal{V}$ on $X$. For an arbitrary band variety $\mathcal{V}$ and an arbitrary set $X$, we determine the group of automorphisms of $\mathrm{End}(B_{\mathcal{V}}(X))$, the monoid of endomorphisms of $B_{\mathcal{V}}(X)$.