We show that if a single algebra has a difference term, then many definitions of the commutator coincide. In particular, this applies to the usual TC-commutator, to the 2-terms commutator and to all the n-ary (cyclic) generalizations we shall introduce. However, we show that there is an algebra in a locally finite variety which is abelian in the sense of the cyclic commutators but not abelian in the sense of the linear commutator (i.e., not quasi-affine). In particular, these commutators are generally distinct.

Lipparini, P. (1996). Difference terms and commutators [Altro].

Difference terms and commutators

P. Lipparini
1996-05-01

Abstract

We show that if a single algebra has a difference term, then many definitions of the commutator coincide. In particular, this applies to the usual TC-commutator, to the 2-terms commutator and to all the n-ary (cyclic) generalizations we shall introduce. However, we show that there is an algebra in a locally finite variety which is abelian in the sense of the cyclic commutators but not abelian in the sense of the linear commutator (i.e., not quasi-affine). In particular, these commutators are generally distinct.
Altro
mag-1996
Privately circulated in preliminary version since April 1994. Available online since 2006. Occasionally quoted
Rilevanza internazionale
Settore MAT/02 - ALGEBRA
English
difference term; commutator; linear commutator; cyclic commutator; quasi-affine algebra
http://axp.mat.uniroma2.it/~lipparin/art/dtcm.pdf
Lipparini, P. (1996). Difference terms and commutators [Altro].
Lipparini, P
Altro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/220200
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