(Co)associative $3$-ary (co)algebras and infinitesimal bialgebras: construction and main properties
Mahouton Norbert Hounkonnou, Gb\^ev\`ewou Damien Houndedji
TL;DR
This paper introduces and analyzes various types of 3-ary (co)algebras and infinitesimal bialgebras, focusing on their construction, properties, and structural relations.
Contribution
It constructs new classes of 3-ary (co)algebras and infinitesimal bialgebras, providing their definitions, properties, and characterizations of modules and matched pairs.
Findings
Constructed new classes of 3-ary (co)algebras and bialgebras.
Characterized trimodules and matched pairs.
Analyzed structural properties and relations.
Abstract
The (co)associative, partially (co)associative and totally (co)associative -ary (co) algebras and infinitesimal bialgebras are constructed and discussed. Their trimodules and matched pairs are defined and completely characterized. The main structural properties and relations are also deduced and analyzed.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology