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E. Peyghan

Publications and source records attributed to E. Peyghan.

At least 19 recordsLinked to original sources
arXiv2024

Formal deformations and extensions of `twisted' Lie algebras

The interplay between derivations and algebraic structures has been a subject of significant interest and exploration. Inspired by Yau's twist and the Leibniz rule, we investigate the formal deformation of twisted Lie algebras by invertible derivations, herein referred to as "InvDer Lie". We define representations of InvDer Lie, elucidate cohomology structures of order 1 and 2, and identify infinitesimals as 2-cocycles. Furthermore, we explore central extensions of InvDer Lie, revealing their intricate relationship with cohomology theory.

math.RA↗
arXiv2021

Representations and Deformations of 3-Hom-$ρ$-Lie algebras

The aim of this paper is to introduce 3-Hom-$ρ$-Lie algebra structures generalizing the algebras of 3-Hom-Lie algebra. Also, we investigate the representations and deformations theory of this type of Hom-Lie algebras. Moreover, we introduce the definition of extensions and abelian extensions of 3-Hom-$ρ$-Lie algebras and show that associated to any abelian extension, there is a representation and a 2-cocycle.

math.RA↗
arXiv2020

Kähler-Norden structures on Hom-Lie group and Hom-Lie algebras

In the present paper, we describe two geometric notions, holomorphic Norden structures and Kähler-Norden structures on Hom-Lie groups, and prove that on Hom-Lie groups in the left invariant setting, these structures are related to each other. We study Kähler-Norden structures with abelian complex structures and give the curvature properties of holomorphic Norden structures on Hom-Lie groups. Finally, we show that any left-invariant holomorphic Hom-Lie group is a flat (holomorphic Norden Hom-Lie algebra carries a Hom-Left-symmetric algebra) if its left-invariant complex structure (complex structure) is abelian.

math.DG↗
arXiv2018

Para-Kahler hom-Lie algebroids

The purpose of this paper is to study hom-algebroids, among them left symmetric hom-algebroids and symplectic hom-algebroids by providing some characterizations and geometric interpretations. Therefore, we introduce and study para-Kähler hom-Lie algebroids and show various properties and examples including these structures.

math.RT↗
arXiv2016

Complex and Kahler structures on hom-Lie algebras

Complex and Hermitian structures on hom-Lie algebras are introduced and some examples of these structures are presented. Also, it is shown that there not exists a proper complex (Hermitian) home-Lie algebra of dimension two. Then using a hom-left symmetric algebra, a phase space is provided and then a complex structure on it, is presented. Finally, the notion of Kahler hom-Lie algebra is introduced and then using a Kahler hom-Lie algebra, a phase space is constructed.

math.RA↗
arXiv2016

Para-Kahler hom-Lie algebras

In this paper, we introduce the notions of pseudo-Riemannian, para-Hermitian and para- Kahler structures on hom-Lie algebras. In addition, we present the characterization of these structures. Also, we provide an example including these structures. We then introduce the phase space of a hom-Lie algebra and using the hom-left symmetric product, we show that a para-Kahler hom-Lie algebra gives a phase space and conversely, we can construct a para-Kahler hom-Lie algebra using a phase space.

math.DG↗
arXiv2016

Weak and strong structures and the $T_{3.5}$ property for generalized topological spaces

We investigate weak and strong structures for generalized topological spaces, among others products, sums, subspaces, quotients, and the complete lattice of generalized topologies on a given set. Also we introduce $T_{3.5}$ generalized topological spaces and give a necessary and sufficient condition for a generalized topological space to be a $T_{3.5}$ space: they are exactly the subspaces of powers of a certain natural generalized topology on $[0,1]$. For spaces with at least two points here we can have even dense subspaces. Also, $T_{3.5}$ generalized topological spaces are exactly the dense subspaces of compact $T_4$ generalized topological spaces. We show that normality is productive for generalized topological spaces. For compact generalized topological spaces we prove the analogue of the Tychonoff product theorem. We prove that also Lindelöfness (and $κ$-compactness) is productive for generalized topological spaces. On any ordered set we introduce a generalized topology and determine the continuous maps between two such generalized topological spaces: for $|X|, |Y| \ge 2$ they are the monotonous maps continuous between the respective order topologies. We investigate the relation of sums and subspaces of generalized topological spaces to ways of defining generalized topological spaces.

math.GN↗
arXiv2016

Exterior differential calculus in generalized Lie algebras(algebroids) category with applications to interior and exterior algebraic(differential) systems

A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the category of generalized Lie algebroids are presented. An exterior differential calculus on generalized Lie algebras is pre- sented and a theorem of Maurer-Cartan type is obtained. Supposing that any submodule(vector subbundle) of a generalized Lie algebra(algebroid) is an interior algebraic(differential) system (IAS(IDS)) for that generalized Lie algebra/algebroid, then the involutivity of the IAS(IDS) in a result of Frobenius type is characterized. Introducing the notion of exterior algebraic(differential) system of a generalized Lie algebra(algebroid), the involutivity of an IAS(IDS) is characterized in a result of Cartan type. Finally, new directions by research in algebraic(differential) symplectic spaces theory are presented.

math.DG↗
arXiv2014

Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality

Supplementary comments about generalized Lie algebroids are presented and a new point of view over the construction of the Lie algebroid generalized tangent bundle of a (dual) vector bundle is introduced. Using the general theory of exterior differential calculus for generalized Lie algebroids, a covariant derivative for exterior forms of a (dual) vector bundle is introduced. Using this covariant derivative, the complete lift of an arbitrary section of a (dual) vector bundle is discovered. A theory of Legendre type and Legendre duality between vertical and complete lifts is presented. Finally, a duality between Lie algebroids structures is developed.

math.DG↗
arXiv2014

On Kropina Change of m-th Root Finsler Metrics

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.

math.DG↗
arXiv2014

Weyl's Theory in the Generalized Lie Algebroids Framework

The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Formulas of Ricci type and identities of Cartan and Bianchi type are presented. Introducing the notion of geodesic of a mechanical $\left( ρ,η\right) $-system with respect to a $(ρ, η)$-spray, the Berwald $(ρ, η)$-derivative operator and its mixed curvature, we obtain main results to conceptualize the Weyl's method in this general framework. Finally, we obtain two new results of Weyl type for the geometry of mechanical $\left( ρ,η\right) $-systems.

math.DG↗
arXiv2014

On the Second Approximate Matsumoto Metric

In this paper, we study the second approximate Matsumoto metric on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.

math.DG↗
arXiv2014

(Pseudo)Generalized Kaluza-Klein G-Spaces and Einstein Equations

Introducing the Lie algebroid generalized tangent bundle of a Kaluza-Klein bundle, we develop the theory of general distinguished linear connections for this space. In particular, using the Lie algebroid generalized tangent bundle of the Kaluza-Klein vector bundle, we present the $\left( g,h\right) $-lift of a curve on the base $M$ and we characterize the horizontal and vertical parallelism of the $\left( g,h\right) $-lift of accelerations with respect to a distinguished linear $\left( ρ,η\right) $-connection. Moreover, we study the torsion, curvature and Ricci tensor field associated to a distinguished linear $\left( ρ,η\right) $-connection and we obtain the identities of Cartan and Bianchi type in the general framework of the Lie algebroid generalized tangent bundle of a Kaluza-Klein bundle. Finally, we introduce the theory of (pseudo) generalized Kaluza-Klein G-spaces and we develop the Einstein equations in this general framework.

math-ph↗
arXiv2014

Some Results Related to Soft Topological Spaces

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft separation axioms that have been studied by Min and Shabir-Naz. By constructing a special soft topological space, show that some classical results in general topology are not true about soft topological spaces, for instance every compact Housdorff spaces need not be normal.

math.GM↗
arXiv2013

Tensor sphere bundle of Cheeger-Gromoll type

We construct a metrical framed structure on the tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric and by restricting this structure to the tensor sphere bundle, we obtain an almost metrical paracontact structure on the tensor sphere bundle. Moreover, we show that the tensor sphere bundles endowed with the induced metric are never space forms.

math.DG↗
arXiv2013

Generalized P-Reducible Finsler Metrics

In this paper, we study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalize Matsumotos theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible.

math.DG↗