arXiv subjects
Publications and source records attributed to Batkam Mbatchou V. Jacky III.
In this work, we introduce a new class of Leibniz algebras, called quasi-Artinian Leibniz algebras, which generalizes the minimal condition on ideals. Furthermore, we provide some characterizations and give conditions under which a quasi-Artinian Leibniz algebra is Artinian. Finally, within the framework of Leibniz algebras, we establish a connection between prime ideals and the quasi-Artinian structure.
Motivated by the recent work of Batkam-Tcheka on pointed multiplicative operads, we construct in this paper new chain complex algebras and two distinct bicomplex algebra structures on a free symmetric connected multiplicative differential graded operad. Furthermore, we focus on the non-differential graded case and construct a differential graded Hopf algebra structure using the odot product together with an analogue of the Alexander-Whitney homomorphism and a compatible differential. As a consequence, we extend the Malvenuto-Reutenauer result by showing that every free symmetric connected multiplicative operad naturally carries a differential graded Hopf algebra structure.