Lie-admissible coalgebras

Abstract

After introducing the concept of Lie-admissible coalgebras, we study a remarkable class corresponding to coalgebras whose coassociator satisfies invariance conditions with respect to the symmetric group Σ 3 . We then study the convolution and tensor products.2000 MSC: 17D25, 16W30

Generalization of n-ary Nambu algebras and beyond

“…We introduced Hom-coalgebra structure, leading to the notions of Hom-bialgebra and Hom-Hopf algebra, proved some fundamental properties and provided examples. Also, we defined the concept of Hom-Lie admissible Hom-coalgebra generalizing the admissible coalgebra introduced in [29], and provide their classification based on subgroups of the symmetric group. This paper is organized as follows.…”

Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras

“…where the bullet • denotes the multiplication on tensor product and by using the Sweedler's notation ∆ (x) = (x) x (1) ⊗ x (2) . If there is no ambiguity we denote the multiplication by a dot.…”

“…In the present paper we develop the coalgebra counterpart of the notions and results of [12], extending in particular in the framework of Hom-associative and Hom-Lie algebras and Hom-coalgebras, the notions and results on associative and Lie admissible coalgebras obtained in [2]. In the first section we summarize the relevant definitions of Hom-associative algebra, Hom-Lie algebra, Hom-Leibniz algebra, and define the notions of Hom-coalgebras and Hom-coassociative coalgebras.…”

Hom-center-symmetric algebras and bialgebras

“…The algebraic properties of hom-coalgebras, hom-coassociative coalgebras, and G -homcoalgebras, where G is a subgroup of the permutation group S 3 [11] generalizing Lie-admissible coalgebras, were investigated in [5]. In these works, relevant definitions and properties of hom-Hopf algebras generalizing Hopf algebras, and giving the module and comodule structures over hom-associative algebras and hom-coassociative coalgebras, were given.…”