## Supernilpotent Taylor algebras are nilpotent

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- by Andrew Moorhead PDF
- Trans. Amer. Math. Soc.
**374**(2021), 1229-1276 Request permission

## 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.## References

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## Additional Information

**Andrew Moorhead**- Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37212
- MR Author ID: 1285442
- ORCID: 0000-0002-7117-1400
- Email: apmoorhead@gmail.com
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 1229-1276 - MSC (2020): Primary 08A40; Secondary 08A05, 08B05
- DOI: https://doi.org/10.1090/tran/8251
- MathSciNet review: 4196392