Hom-Big Brackets: Theory and Applications

Cai, Liqiang; Sheng, Yunhe

doi:10.3842/sigma.2016.014

Cited by 17 publications

(25 citation statements)

References 30 publications

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“…, which is the same as the condition given in [6,Proposition 6.2]. Thus, the notion of a Hom-Nijenhuis operator of an n-Hom-Lie algebra is a natural generalization of the Hom-Nijenhuis operator of a Hom-Lie algebra given in [6].…”

Section: Definition 44mentioning

confidence: 89%

Cohomologies, deformations and extensions of n-Hom-Lie algebras

Song

Tang

2019

Journal of Geometry and Physics

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In this paper, first we give the cohomologies of an n-Hom-Lie algebra and introduce the notion of a derivation of an n-Hom-Lie algebra. We show that a derivation of an n-Hom-Lie algebra is a 1-cocycle with the coefficient in the adjoint representation. We also give the formula of the dual representation of a representation of an n-Hom-Lie algebra. Then, we study (n − 1)-order deformation of an n-Hom-Lie algebra. We introduce the notion of a Hom-Nijenhuis operator, which could generate a trivial (n − 1)-order deformation of an n-Hom-Lie algebra. Finally, we introduce the notion of a generalized derivation of an n-Hom-Lie algebra, by which we can construct a new n-Hom-Lie algebra, which is called the generalized derivation extension of an n-Hom-Lie algebra.

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Section: Definition 44mentioning

confidence: 89%

Cohomologies, deformations and extensions of n-Hom-Lie algebras

Song

Tang

2019

Journal of Geometry and Physics

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“…We give a generalization to Hom-Lie algebras of the grand crochet defined by Lecomte and Roger [LR90]. For the case β = α −1 this was already done in [CS16].…”

Section: Grand Crochetmentioning

confidence: 99%

“…In the associative case a cohomology for Hom-bialgebras has been defined in [DM17]. This allows us to write down in an easy way the cohomology for Hom-Lie bialgebras with fixed structure map for an example studied in a less general case in [CS16].…”

Section: Introductionmentioning

confidence: 99%

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α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS

Hurle¹,

Makhlouf²

2019

Glasgow Math. J.

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The purpose of this paper is to define an α-type cohomology, which we call α-type Chevalley-Eilenberg cohomology, for Hom-Lie algebras. We relate it to the known Chevalley-Eilenberg cohomology and provide explicit computations for some examples. Moreover, using this cohomology we study formal deformations of Hom-Lie algebras, where the bracket as well as the structure map α are deformed. Furthermore, we provide a generalization of the Grand Crochet and study, in a particular case, the α-type cohomology for Hom-Lie bialgebras.

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“…According to the literature [18], we know that the relationship between the time and survival of the affected people in earthquake is…”

Section: Mathematical Modelmentioning

confidence: 99%

Research on Improved NSGA-II Algorithm and Its Application in Emergency Management

Fang

Wang

et al. 2018

Mathematical Problems in Engineering

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This paper constructs a dynamic multiobjective location model; three objectives are considered: the first objective maximizes the total utility of relief supplies, the second objective minimizes the number of temporary facilities needed to operate, and the third objective maximizes the satisfaction for all demand points. We propose an improved NSGA-II to solve the optimization problem. The computational experiments are divided into two sections: In the first procedure, the numerical experiment is constructed by the classical functions ZDT1, ZDT2, and DTLZ2; the results show that the proposed algorithm generates the exact Pareto front, and the convergence and uniformity of the proposed algorithm are better than the NSGA-II and MOEA/D. In the second procedure, the simulation experiment is constructed by a case in emergency management; the results show that the proposed algorithm is more reasonable than the traditional algorithms NSGA-II and MOEA/D in terms of the three objectives. It is proved that the improved NSGA-II algorithm, which is proposed in this paper, has high precision application for the sudden disaster crisis and emergency management.

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Hom-Big Brackets: Theory and Applications

Cited by 17 publications

References 30 publications

Cohomologies, deformations and extensions of n-Hom-Lie algebras

Cohomologies, deformations and extensions of n-Hom-Lie algebras

α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS

Research on Improved NSGA-II Algorithm and Its Application in Emergency Management

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