Pith. sign in

REVIEW 1 cited by

On Nilpotent Triassociative Algebras

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2306.15059 v2 pith:DWS5UHVV submitted 2023-06-26 math.RA

Sona Baghiyan , Liam Gallagher , Erik Mainellis This is my paper · ORCID
classification math.RA
keywords nilpotentalgebrastriassociativemultiplicationsotherthreealgebraalone
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the current paper, we present a study of nilpotent triassociative algebras. After some examples and basic results, we provide a low-dimensional classification, a general monomial form, and an analogue of Engel's Theorem. The main result shows that one of the three multiplication operations behaves differently than the other two. In particular, if this structure alone is nilpotent, then both other multiplications are nilpotent. The converse is not true. Furthermore, the former is nilpotent if and only if the entire algebra is nilpotent.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Crossed modules of ternary Leibniz algebras

    math.RA 2025-01 reject novelty 4.0 of 10

    The paper transfers crossed modules from triassociative and Leibniz algebras to ternary Leibniz algebras, but omits the supporting computations and contains garbled formulas.

Pith tools