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After endowing with a 3-Lie-Rinehart structure on Hom 3-Lie algebras, we obtain a class of special Hom 3-Lie algebras, which have close relationships with representations of commutative associative algebras. We provide a special class of…

Rings and Algebras · Mathematics 2020-01-24 Ruipu Bai , Xiaojuan Lie , Yingli Wu

We study hom-associative structures on general possibly non-associative algebras focusing on one-sided and two-sided unital algebras. New characterizations and aspects of these structures, along with some important subclasses, are explored…

Rings and Algebras · Mathematics 2026-03-27 Germán García Butenegro , Abdennour Kitouni , Sergei Silvestrov

A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.

Rings and Algebras · Mathematics 2012-01-24 K. R. Goodearl

Hom-Lie algebras are non-associative algebras generalizing Lie algebras by twisting the Jacobi identity by an endomorphism. The main examples are algebras of twisted derivations (i.e., linear maps with a generalized Leibniz rule). Such…

Algebraic Geometry · Mathematics 2014-01-31 Daniel Larsson

An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…

Rings and Algebras · Mathematics 2014-03-20 James Griffin

Let $H$ be a cocommutative Hopf algebra. The notion of Lie $H$-pseudoalgebra is a multivariable generalization of Lie conformal algebras. In this paper, we study some higher structures related to Lie $H$-pseudoalgebras where we increase the…

Representation Theory · Mathematics 2024-03-19 Apurba Das

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids…

Rings and Algebras · Mathematics 2021-10-27 Anja Arfa , Nejib Saadaoui , Sergei Silvestrov

We describe a new method of quantization of Lie bialgebras, based on a construction of Hopf algebras out of a cocommutative coalgebra and a braided comonoidal functor.

Quantum Algebra · Mathematics 2017-06-23 Pavol Ševera

This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule…

Rings and Algebras · Mathematics 2019-08-26 Sylvain Attan

The aim of this paper is to transfer the restrictedness theory to Hom-Lie algebras. The concept of restricted Hom-Lie algebras which is introduced in \cite{BM2} will be used in this paper. First, the existence of $p$-structures on a Hom-Lie…

Rings and Algebras · Mathematics 2023-12-01 Dan Mao , Baoling Guan , Liangyun Chen

Some basic properties of Hom-Leibniz algebras are found. These properties are the Hom-analogue of corresponding well-known properties of Leibniz algebras. Considering the Hom-Akivis algebra associated to a given Hom-Leibniz algebra, it is…

Rings and Algebras · Mathematics 2010-11-09 A. Nourou Issa

Let F denote the homotopy fiber of a map f:K-->L of 2-reduced simplicial sets. Using as input data the strongly homotopy coalgebra structure of the chain complexes of K and L, we construct a small, explicit chain algebra, the homology of…

Algebraic Topology · Mathematics 2014-10-01 Kathryn Hess , Ran Levi

We develop versions of the Poincar\'e-Birkhoff-Witt and Cartier-Milnor-Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogues of a Lie algebra in the setting of a braided monoidal category, using the…

Quantum Algebra · Mathematics 2025-10-14 Craig Westerland

We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal category. Thus we unify all different types of Hopf cyclic (co)homologies under one single universal theory. We recover Hopf cyclic (co)homology of module…

K-Theory and Homology · Mathematics 2007-05-23 Atabey Kaygun

The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…

Rings and Algebras · Mathematics 2017-10-23 Anja Arfa , Nizar Ben Fraj , Abdenacer Makhlouf

We construct symmetric monoidal categories $\LRF, \FD$ of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf…

Quantum Algebra · Mathematics 2009-11-13 Kobi Kremnizer , Matthew Szczesny

This paper introduces Hom-type analogues of affine algebraic structures, termed Hom-affgebras. Extending Brzezi\'nski's theory of affgebras and the Hom-algebra framework developed by Hartwig-Larsson-Silvestrov, we define and study…

Rings and Algebras · Mathematics 2025-11-06 Tarik Anowar , Ripan Saha

In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology…

K-Theory and Homology · Mathematics 2015-12-09 Mohammad Hassanzadeh , Ilya Shapiro , Serkan Sütlü

The aim of this paper is to introduce the notion of restricted Hom- Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to…

Rings and Algebras · Mathematics 2022-11-02 Shadi Shaqaqha

We introduce and study Hopf monads on autonomous categories (i.e., monoidal categories with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) setting. Indeed, any monoidal adjunction between autonomous…

Quantum Algebra · Mathematics 2007-05-23 Alain Bruguières , Alexis Virelizier