In this paper, we study universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras. We discuss $\alpha $-central extensions, the lifting automorphisms $-derivations to hom-Li

Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in [62]. In this paper, several more classes of solutions of the HYBE are constructed. Some of these solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drin...

The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of Γ-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one paramete...

In this paper we study the homotopy type of Hom (Cm, Cn), where Ck is the cyclic graph with k vertices. We enumerate connected components of Hom (Cm, Cn) and show that each such component is either homeomorphic to a point or homotopy equivalent to S1. Moreover, we prove that Hom (Cm, Ln) is either empty or is homotopy equivalent to the union of two points, where Ln is an n-string, i.e., a tree ...

In this paper we study the homotopy type of Hom (Cm, Cn), where Ck is the cyclic graph with k vertices. We enumerate connected components of Hom (Cm, Cn) and show that each such component is either homeomorphic to a point or homotopy equivalent to S1. Moreover, we prove that Hom (Cm, Ln) is either empty or is homotopy equivalent to the union of two points, where Ln is an n-string, i.e., a tree ...

Hom (G,H) is a polyhedral complex defined for any two undirected graphs G and H. This construction was introduced by Lovász to give lower bounds for chromatic numbers of graphs. In this paper we initiate the study of the topological properties of this class of complexes. We prove that Hom (Km,Kn) is homotopy equivalent to a wedge of (n−m)dimensional spheres, and provide an enumeration formula f...