Article
Mathematics
Taoufik Chtioui, Sami Mabrouk, Abdenacer Makhlouf
Summary: This paper introduces the cohomology theory of O operators on Hom-associative algebras, studies the deformations of O operators and their relation with cohomology, and introduces the notion of Nijenhuis elements to characterize trivial deformations. It also provides relevant constructions for twisting objects from associative algebras to Hom-associative algebras along morphisms.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics, Applied
Goutam Mukherjee, Ripan Saha
Summary: The aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras and apply it to control deformations of these algebras. The research is further extended to the equivariant context, where finite group actions on the algebras are considered.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2022)
Article
Mathematics
Shanshan Liu, Abdenacer Makhlouf, Lina Song
Summary: The main purpose of this paper is to study the cohomology of Hom-pre-Lie algebras with coefficients in a given representation, and to show its classification properties.
ELECTRONIC RESEARCH ARCHIVE
(2022)
Article
Mathematics, Applied
Yu Xiu Bai, Leonid A. Bokut, Yu Qun Chen, Ze Rui Zhang
Summary: In this article, we construct free centroid hom-associative algebras and free centroid hom-Lie algebras. We also construct some other relatively free centroid hom-associative algebras using the Groebner-Shirshov basis theory. Finally, we prove that the Poincare-Birkhoff-Witt theorem holds for a certain type of centroid hom-Lie algebras over a field of characteristic 0.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2023)
Article
Mathematics
Lina Song, Shuang Lai, Shanshan Liu
Summary: In this paper, we use the cohomological approach to study abelian extensions and formal deformations of Hom-pre-Lie algebras. We show that diagonal abelian extensions of Hom-pre-Lie algebras can be classified by stable points in the second cohomology group under the action of an isomorphism. The infinitesimals of two equivalent formal deformations of a Hom-pre-Lie algebra A are in the same cohomological class in H-2(A; A), and if H-2(A; A) is trivial, then the Hom-pre-Lie algebra A is rigid.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics
Apurba Das, Sourav Sen
Summary: This article studies Nijenhuis operators on Hom-Lie algebras, constructs a graded Lie algebra, and explores the cohomology associated with Nijenhuis operators. Formal deformations of Nijenhuis operators are generated by the defined cohomology. The introduction of Hom-NS-Lie algebras provides an algebraic structure behind Nijenhuis operators on Hom-Lie algebras.
COMMUNICATIONS IN ALGEBRA
(2022)
Article
Mathematics, Applied
Wen Teng, Jiulin Jin, Yu Zhang
Summary: In this paper, we generalize known results of nonabelian embedding tensor to the Hom setting. We introduce the concept of Hom-Leibniz-Lie algebra, which is the basic algebraic structure of nonabelian embedded tensors on Hom-Lie algebras and can also be regarded as a nonabelian generalization of Hom-Leibniz algebra. Moreover, we define a cohomology of nonabelian embedding tensors on Hom-Lie algebras with coefficients in a suitable representation. The first cohomology group is used to describe infinitesimal deformations as an application. In addition, Nijenhuis elements are used to describe trivial infinitesimal deformations.
Article
Mathematics, Applied
Shadi Shaqaqha
Summary: In this study, we aimed to familiarize ourselves with the concept of fuzzy Hom-Lie subalgebras (ideals) of Hom-Lie algebras, and to study some of their properties. The research examines the relationship between fuzzy Hom-Lie subalgebras (ideals) and Hom-Lie subalgebras (ideals). Additionally, new fuzzy Hom-Lie subalgebras are constructed based on the direct sum of a finite number of existing ones. Finally, the properties of fuzzy Hom-Lie subalgebras and fuzzy Hom-Lie ideals are examined in the context of the morphisms of Hom-Lie algebras.
Article
Mathematics
Erica Z. Fornaroli, Mykola Khrypchenko, Ednei A. A. Santulo Jr
Summary: We fully characterize regular Hom-Lie structures on the incidence algebra I(X, K) of a finite connected poset X over a field K. We prove that such a structure is the sum of a central-valued linear map annihilating the Jacobson radical of I(X, K) with the composition of certain inner and multiplicative automorphisms of I(X, K).
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics, Applied
Esmaeil Peyghan, Aydin Gezer, Zahra Bagheri, Inci Gultekin
Summary: The aim of this paper is to introduce 3-Hom-rho-Lie algebra structures that generalize the algebras of 3-Hom-Lie algebra. The representations and deformations theory of this type of Hom-Lie algebras are also investigated. Additionally, the definition of extensions and abelian extensions of 3-Hom-rho-Lie algebras are introduced, and it is shown that there is a representation and a 2-cocycle associated with any abelian extension.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics
J. N. Alonso Alvarez, J. M. Fernandez Vilaboa, R. Gonzalez Rodriguez
Summary: This paper introduces the Hom-analogue of 2-co cycle for Hopf algebras, known as Hom-2-co cycle, and studies its properties in the context of multiplication alteration and skew pairing in Hom-Hopf algebras.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
Maria Alejandra Alvarez, Sonia Vera
Summary: This work focuses on obtaining all rigid complex 3-dimensional multiplicative Hom-Lie algebras by studying deformations of multiplicative Hom-Lie algebras that are also Lie algebras. Additionally, the well-known classification of 3-dimensional multiplicative (non-Lie) Hom-Lie algebras is derived as a byproduct.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Shuangjian Guo, Ripan Saha
Summary: In this paper, a new cohomology theory is defined for multiplicative Hom-pre-Lie algebras to control deformations of their algebraic structure. By considering the structure map, this theory is a natural one. Equivariant cohomology theory for Hom-pre-Lie algebras equipped with a finite group action is developed by formulating a proper notion of coefficients system. The associated formal deformation theory for Hom-pre-Lie algebras in the equivariant context is also studied.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics
Jose Manuel Casas, Seyedeh Narges Hosseini
Summary: The concept of Hom-isoclinism of central extensions of Hom-Lie algebras is introduced and studied in this article. It is used to describe the Schur multiplier of Hom-Lie algebras, determine the structure of Hom-stem covers, and establish a relation between Hom-stem covers and the universal central extensions of perfect Hom-Lie algebras.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics, Applied
E. Peyghan, L. Nourmohammadifar
Summary: This paper focuses on Horn-Lie groups and investigates left invariant almost contact structures (almost contact Horn-Lie algebras) on them. It constructs almost contact metrics and contact forms on such Horn-Lie groups. The concept of normal almost contact Hom-Lie algebras is introduced, and K-contact and Sasakian structures on Hom-Lie algebras are described and studied.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Statistics & Probability
Dmitrii Silvestrov, Sergei Silvestrov
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
(2019)
Article
Mathematics
Abdoreza Armakan, Sergei Silvestrov, Mohammad Reza Farhangdoost
Summary: This paper investigates the extensions of hom-Lie color algebras, providing a geometrical interpretation and discussing cohomological obstructions to their existence.
GEORGIAN MATHEMATICAL JOURNAL
(2021)
Article
Mathematics, Applied
Tianshui Ma, Abdenacer Makhlouf, Sergei Silvestrov
Summary: In this paper, a dual version of T. Brzezinski's results on Rota-Baxter systems is presented, along with various examples of Rota-Baxter bialgebras and bisystems in dimensions 2, 3, and 4. Additionally, a new type of bialgebras called mixed bialgebras is introduced, and the properties of coquasitriangular mixed bialgebras and coquasitriangular infinitesimal bialgebras are investigated, with the potential for obtaining Rota-Baxter cosystems.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Viktor Abramov, Sergei Silvestrov
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
(2020)
Article
Statistics & Probability
Dmitrii Silvestrov, Sergei Silvestrov, Benard Abola, Pitos Seleka Biganda, Christopher Engstrom, John Magero Mango, Godwin Kakuba
Summary: This paper focuses on regularly and singularly perturbed Markov chains with a damping component, where transition probabilities are regularized by adding a damping matrix multiplied by a small perturbation parameter epsilon. Perturbation analysis is performed, providing upper bounds for approximation rates, asymptotic expansions, explicit coupling type upper bounds for convergence rates in ergodic theorems, and ergodic theorems in triangular array mode.
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
(2021)
Article
Mathematics, Applied
Sami Mabrouk, Othmen Ncib, Sergei Silvestrov
Summary: This paper generalizes the construction of n-ary Hom-Lie bracket using an (n-2)-cochain of given HomLie algebra, leading to n-Hom-Lie superalgebras; it examines the concepts of generalized derivations and Rota-Baxter operators in n-ary Hom-Nambu and n-Hom-Lie superalgebras, and their relationship with those in Hom-Lie superalgebras; additionally, the notion of 3-Hom-pre-Lie superalgebras is introduced as a generalization of 3-Hom-pre-Lie algebras.
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
(2021)
Article
Mathematics
Abdelkader Ben Hassine, Taoufik Chtioui, Sami Mabrouk, Sergei Silvestrov
Summary: The concept of 3-Lie-Rinehart superalgebra is introduced and a cohomology complex is systematically described with consideration of coefficient modules. Furthermore, the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra are studied, along with the deformations of the latter through a cohomology theory.
COMMUNICATIONS IN ALGEBRA
(2021)
Article
Mathematics
M. Elhamdadi, A. Makhlouf, S. Silvestrov, E. Zappala
Summary: This paper introduces and investigates the concept of derivation for quandle algebras. It provides a characterization for derivations and obtains the dimensionality of the Lie algebra of derivations. The paper includes explicit examples and computations for both zero and positive characteristic, and also explores inner derivations for non-associative structures.
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
(2022)
Article
Physics, Mathematical
Fattoum Harrathi, Sami Mabrouk, Othmen Ncib, Sergei Silvestrov
Summary: The paper introduces and studies a Hom-type generalization of pre-Malcev algebras called Hom-pre-Malcev algebras, which have twisted identities defined by linear maps. The connections between Hom-Malcev and Hom-pre-Malcev algebras are explored using Kupershmidt operators. Hom-pre-Malcev algebras generalize Hom-pre-Lie algebras and have a close relationship with Hom-pre-alternative algebras. Additionally, a deformation theory of Kupershmidt operators on Hom-Malcev algebras is established, consistent with general principles of deformation theories, and the concept of Nijenhuis elements is introduced.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2023)
Article
Mathematics, Applied
Mohammed Reza Farhangdoost, Ahmad Reza Attari Polsangi, Sergei Silvestrov
Summary: This paper considers complete hom-Lie superalgebras and establishes some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra. In particular, the relation between decomposition and completeness for a hom-Lie superalgebra is described. Moreover, some conditions for the linear space of alpha(s)-derivations of a hom-Lie superalgebra to be complete and simply complete are obtained.
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
(2023)
Article
Mathematics
Ismail Laraiedh, Sergei Silvestrov
Summary: This paper introduces the notion of Hom-Leibniz bialgebra and shows that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras, and Hom-Leibniz bialgebras are equivalent in a certain sense. It establishes the concept of Hom-Leibniz dendriform algebra, defines their bimodules and matched pairs, and obtains properties and theorems about their interplay and construction. Furthermore, it introduces and discusses the concept of BiHom-Leibniz dendriform algebras, constructs their bimodules and matched pairs, and describes their properties. Finally, it demonstrates the connections between all these algebraic structures using O-operators.
Article
Mathematics, Applied
I. Laraiedh, S. Silvestrov
Summary: This paper introduces and develops several methods for constructing BiHom-X algebras, focusing on extending composition methods, utilizing Rota-Baxter operators, and incorporating centroids. It defines the bimodules of BiHom-left symmetric dialgebras, BiHom-associative dialgebras, and BiHom-tridendriform algebra, and demonstrates the construction of sequences of these bimodules. Furthermore, it introduces the matched pairs of BiHom-left symmetric, BiHom-associative dialgebras, and BiHom-tridendriform algebra, and explores methods for their constructions and properties.
ALGEBRA AND DISCRETE MATHEMATICS
(2022)
Article
Mathematics
Ibrahima Bakayoko, Sergei Silvestrov
Summary: This paper introduces and studies constructions and properties of Hom-left-symmetric color dialgebras and Hom-tridendriform color algebras, as well as their connections with other Hom algebras. Additionally, the paper generalizes Yau's twisting to a class of color Hom-algebras and shows how to generate other color Hom-algebras using endomorphisms or elements of centroids from a given one.
Proceedings Paper
Engineering, Electrical & Electronic
V Javor, K. Lundengard, M. Rancic, S. Silvestrov
2019 14TH INTERNATIONAL CONFERENCE ON ADVANCED TECHNOLOGIES, SYSTEMS AND SERVICES IN TELECOMMUNICATIONS (TELSIKS 2019)
(2019)
Proceedings Paper
Mathematics, Applied
Elvice Ongong'a, Johan Richter, Sergei Silvestrov
XXVI INTERNATIONAL CONFERENCE ON INTEGRABLE SYSTEMS AND QUANTUM SYMMETRIES
(2019)
