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...

should hold for X smooth proper, where CH(X)Q is the Chow group of X with rational coefficients, and QX denotes the constant object in D MM(X), the bounded derived category of MM(X). In this paper we give a formalism of mixed sheaves which might be useful for the construction of mixed motivic sheaves. Let k be a field embeddable in C, and V(k) the category of separated algebraic varieties over ...

In terms of category theory, the Gromov homotopy principle for a set valued functor F asserts that the functor F can be induced from a homotopy functor. Similarly, we say that the bordism principle for an abelian group valued functor F holds if the functor F can be induced from a (co)homology functor. We examine the bordism principle in the case of functors given by bordism groups of solutions ...

Applicative functors [6] are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell [5]. Applicative functors are to be preferred to monads when the structure of a computation is fixed a priori. That makes it possible to perform certain kinds of static analysis on applicative values. We define a notion of free applicative fu...

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...