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SUMMARY:Andrew Moorhead (University of Kansas)
DTSTART:20210520T180000Z
DTEND:20210520T190000Z
DTSTAMP:20260423T021248Z
UID:OLS/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/51/">Hig
 her commutators\, hypercubes\, and the hierarchy of centralizer conditions
 </a>\nby Andrew Moorhead (University of Kansas) as part of Online logic se
 minar\n\n\nAbstract\nThe commutator had historically been studied for spec
 ific varieties of algebras until Smith found a general definition for a co
 mmutator that worked for any Mal'cev algebra. Since then the commutator ha
 s become an essential part of the general algebraist's toolkit. Bulatov di
 scovered at the beginning of the century that the (binary) commutator can 
 be extended to an infinite sequence of higher arity operations\, no one of
  which are term definable from the others. This discovery has most importa
 ntly led to the distinction between a nilpotent algebra and a 'supernilpot
 ent' algebra. While this distinction is invisible for groups\, supernilpot
 ent Mal'cev algebras share many strong properties with nilpotent groups\, 
 while nilpotent algebras need not. We will discuss the extent to which som
 e of the known results of commutator theory can be viewed as a low-dimensi
 onal case of a general multidimensional theory.\n
LOCATION:https://researchseminars.org/talk/OLS/51/
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