Peng xiao song

Jiangsu Normal University

In this paper, we first introduce the notion of an extending datum of Rota-Baxter Lie algebras through a vector space. We then construct a unified product for the Rota-Baxter Lie algebra with a vector space as a main ingredient in our approach. Finally, we solve the extending structures problem of Rota-Baxter Lie algebras, which generalizes and uni...

Involving a symmetric Hochschild 1-cocycle condition, we equip the space of decorated planar rooted forests with a coproduct which turns the space into a dendriform-Nijenhuis bialgebra. We combine dendriform-Nijenhuis bialgebras with operated algebras and introduce the notation of an Ω-operated DN-bialgebra. Applying the universal property of the u...

The concept of a weighted infinitesimal unitary bialgebra is an algebraic abstraction of the non-homogeneous associative classical Yang–Baxter equation. In this paper, we equip the free monoid algebra with a suitable coproduct which makes it a weighted infinitesimal unitary bialgebra. Furthermore, by exploring the relationship between weighted infi...

In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras, and matching pre-Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures. 1. Introduction 1.1. Hom-Algebraic Structures The origin of Hom-st...

Involving an extended 1-cocycle condition, we first define a coproduct on the space of bi-decorated planar rooted forests to equip it with a left counital bialgebraic structure. We introduce the concept of left counital (Ω,α )--cocycle bialgebras and show that the space of bi-decorated planar rooted forests is the free object in the category of lef...

We introduce a new operator – a modified λ-differential operator – from a usual differential operator. We construct the free (modified) λ-differential (k,∂)-algebra on a (modified) differential (k,∂)-module, and apply it to erect the universal enveloping (modified) differential algebra of a (modified) λ-differential Lie (k,∂)-algebra. The correspon...

In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures.

In this paper, we construct a complete set of primitive orthogonal idempotents for any finite Brandt semigroup algebra. As applications, we define a new class of codes called Brandt semigroup codes and compute the Cartan matrices of some Brandt semigroup algebras. We also study the supports, Hamming distances, and minimum weights of Brandt semigrou...