ALH-2018

Title. Is supernilpotence super nilpotence?

Speaker. Keith Kearnes

Institution. Department of Mathematics, University of Colorado, Boulder

Abstract. An algebra is nilpotent of class at most 2 if it satisfies the commutator condition $[1,[1,1]]=0$, and it is supernilpotent of class at most 2 if it satisfies the higher commutator condition $[1,1,1]=0$. There are higher-class nilpotence conditions for both commutators. How are they related? From the names, one expects that, for every $k$ there is some $\ell$ such that

class-$k$ supernilpotence = (class-$\ell$ nilpotence + $\varepsilon$)

holds. I will speak about this equation.