scholarly journals Bimultiplications and Annihilators of Crossed Modules in Associative Algebras

2021 ◽  
pp. 72-90
Author(s):  
Ummahan EGE ARSLAN ◽  
Serdar HÜRMETLİ
Keyword(s):  
Associative Algebras ◽  
Crossed Modules

scholarly journals From simplicial homotopy to crossed module homotopy in modified categories of interest

2020 ◽  
Vol 27 (4) ◽  
pp. 541-556
Author(s):  
Kadir Emir ◽  
Selim Çetin
Keyword(s):  
Lie Algebras ◽  
Equivalence Relation ◽  
Crossed Module ◽  
Algebraic Structures ◽  
Homotopy Equivalence ◽  
Associative Algebras ◽  
Leibniz Algebras ◽  
Crossed Modules ◽  
Simplicial Objects ◽  
Simplicial Homotopy

AbstractWe address the (pointed) homotopy of crossed module morphisms in modified categories of interest that unify the notions of groups and various algebraic structures. We prove that the homotopy relation gives rise to an equivalence relation as well as to a groupoid structure with no restriction on either domain or co-domain of the corresponding crossed module morphisms. Furthermore, we also consider particular cases such as crossed modules in the categories of associative algebras, Leibniz algebras, Lie algebras and dialgebras of the unified homotopy definition. Finally, as one of the major objectives of this paper, we prove that the functor from simplicial objects to crossed modules in modified categories of interest preserves the homotopy as well as the homotopy equivalence.

scholarly journals More on crossed modules in Lie, Leibniz, associative and diassociative algebras

2017 ◽  
Vol 16 (06) ◽  
pp. 1750107 ◽  
Author(s):  
J. M. Casas ◽  
R. F. Casado ◽  
E. Khmaladze ◽  
M. Ladra
Keyword(s):  
Associative Algebras ◽  
Adjoint Functors ◽  
Leibniz Algebras ◽  
Crossed Modules

Adjoint functors between the categories of crossed modules in dialgebras and Leibniz algebras are constructed. The well known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the respective categories of crossed modules.

scholarly journals Braiding for categorical algebras and crossed modules of algebras I: Associative and Lie algebras

2019 ◽  
Vol 19 (09) ◽  
pp. 2050176
Author(s):  
A. Fernández-Fariña ◽  
M. Ladra
Keyword(s):  
Lie Algebras ◽  
Associative Algebras ◽  
Crossed Modules

In this paper, the categories of braided categorical associative algebras and braided crossed modules of associative algebras are studied. These structures are also correlated with the categories of braided categorical Lie algebras and braided crossed modules of Lie algebras.

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

scholarly journals Total Differentiability and Monogenicity for Functions in Algebras of Order 4

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
I. Sabadini ◽  
D. C. Struppa
Keyword(s):  
Analytic Functions ◽  
Associative Algebras ◽  
Basic Tool ◽  
Algebraic Analysis ◽  
Italian School ◽  
Relevant Role

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

Sign in / Sign up

Export Citation Format

Share Document