Classification of tridendriform algebra and related structures
Bouzid Mosbahi, Sania Asif, Ahmed Zahari

TL;DR
This paper classifies tridendriform algebras and their derivations and centroids, revealing the structure and diversity of these algebraic objects across various dimensions using computational methods.
Contribution
It provides the first explicit classification of derivations and centroids of tridendriform algebras up to dimension five, including computational analysis of structure constants.
Findings
Only trivial derivations for 2- and 3-dimensional algebras.
21 non-isomorphic derivations for 4-dimensional algebras.
Number of centroid classes varies with dimension, up to 21 for 4-dimensional algebras.
Abstract
The classification of algebraic structures and their derivations is an important and ongoing research area in mathematics and physics, and various results have been obtained in this field. This article presents the classification of tridendriform algebras that was first studied by Loday and Ronco, including an analysis of structure constant equations using computer algebra software. We further explicitly classify the derivations and centroids of tridendriform algebras, showing that there are only trivial derivations for - and -dimensional algebras but non-isomorphic derivations for -dimensional tridendriform algebras with dimension range from to . Additionally, for centroids (centroid and quasi-centroid), there are trivial isomorphism classes for dimensional tridendriform algebra, non-isomorphic classes for -dimensional tridendriform algebras and for…
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Sphingolipid Metabolism and Signaling
