Year: 2025
Type: article
Abstract: We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutative extended diassociative semigroups (briefly, CEDS), which are used to define generalizations of the operad of pre-Lie algebras. We give families of examples based on semigroups or on groups, as well as a classification of EAS of cardinality two. We then define linear extended associative semigroups as linear maps satisfying a variation of the braid equation. We explore links between linear EAS and bialgebras and Hopf algebras. We also study the structure of non-degenerate finite CEDS and show that they are obtained by semi-direct and direct products involving two groups.
Authors: Université Littoral Côte d'Opale, France, Loïc Foissy
Institution: Université du littoral côte d'opale
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4415557706
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