Supernilpotent Taylor algebras are nilpotent
Author:
Andrew Moorhead
Journal:
Trans. Amer. Math. Soc. 374 (2021), 1229-1276
MSC (2020):
Primary 08A40; Secondary 08A05, 08B05
DOI:
https://doi.org/10.1090/tran/8251
Published electronically:
November 12, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We develop the theory of the higher commutator for Taylor varieties. A new higher commutator operation called the hypercommutator is defined using a type of invariant relation called a higher dimensional congruence. The hypercommutator is shown to be symmetric and satisfy an inequality relating nested terms. For a Taylor algebra the term condition higher commutator and the hypercommutator are equal when evaluated at a constant tuple, and it follows that every supernilpotent Taylor algebra is nilpotent. We end with a characterization of congruence meet-semidistributive varieties in terms of the neutrality of the higher commutator.
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Additional Information
Andrew Moorhead
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37212
Email:
apmoorhead@gmail.com
DOI:
https://doi.org/10.1090/tran/8251
Received by editor(s):
June 19, 2019
Received by editor(s) in revised form:
June 21, 2019, and June 11, 2020
Published electronically:
November 12, 2020
Additional Notes:
This work was supported by the National Science Foundation grant no. DMS 1500254 and the Austrian Science Fund (FWF):P29931
Article copyright:
© Copyright 2020
American Mathematical Society