• Korean Journal of Mathematics
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• v.27 no.1
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• pp.175-192
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• 2019

(Multiplicative) Hom-Lie-Yamaguti superalgebras are defined as a ${\mathbb{Z}}_2$-graded generalization of Hom-Lie Yamaguti algebras and also as a twisted generalization of Lie-Yamaguti superalgebras. Hom-Lie-Yamaguti superalgebras generalize also Hom-Lie supertriple systems (and subsequently ternary multiplicative Hom-Nambu superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti superalgebras generalize Lie supertriple systems and Lie superalgebras. Hom-Lie-Yamaguti superalgebras are obtained from Lie-Yamaguti superalgebras by twisting along superalgebra even endomorphisms. We show that the category of (multiplicative) Hom-Lie-Yamaguti superalgebras is closed under twisting by self-morphisms. Constructions of some examples of Hom-Lie-Yamaguti superalgebras are given. The notion of an nth derived (binary) Hom-superalgebras is extended to the one of an nth derived binary-ternary Hom-superalgebras and it is shown that the category of Hom-Lie-Yamaguti superalgebras is closed under the process of taking nth derived Hom-superalgebras.

• Korean Journal of Human Ecology
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• v.17 no.6
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• pp.1079-1091
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• 2008

This study investigated developmental differences of moral evaluation for different lies. The subjects were 170 6-, 8-, and 10-year-olds. Children's understanding of, moral judgment for, and emotional reactions to antisocial lie, white lie, and trick lie were assessed. Major findings were as follows: 1. Children's understanding of lies was increased with age. Children understood well in definition for antisocial lie, whereas they understood poorly in definition for trick lie. 2. There were differences of children's moral judgment for lies according to age and lie types. Six- and 8-year-olds rated trick lie as the least serious lie type, whereas 10-year-olds rated white lie as the least serious lie type. 3. Children anticipated the greatest negative emotional reaction to antisocial lie, and the greatest positive reaction to trick lie by all ages. There was no difference of positive emotional reaction between antisocial lie and white lie for 6- and 8-year-olds. But 10-year-olds anticipated greater positive emotional reaction to white lie than antisocial lie.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.363-373
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• 2022

In this paper we mainly establish a relationship between involutions of multiplicative Hom-Lie algebras and Hom-Lie triple systems. We show that the -1-eigenspace of any involution on any multiplicative Hom-Lie algebra becomes a Hom-Lie triple system and we construct some examples of Hom-Lie triple systems using some involutions of some classical Hom-Lie algebras.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.11-30
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• 2024

3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.259-268
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• 2007

The notion of intuitionistic fuzzy Lie ideal of a Lie algebra is introduced, and related properties are investigated. Characterizations of an intuitionistic fuzzy Lie ideal are provided. Using a collection of Lie ideals, an intuitionistic fuzzy Lie ideal is established.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.305-313
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• 2019

Using the fixed point method, we prove the Hyers-Ulam stability of 3-Lie homomorphisms and 3-Lie derivations in 3-Lie algebras for Cauchy-Jensen functional equation.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1199-1211
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• 2012

In this paper we give an introduction to the theory of universal central extensions of perfect Lie algebras. In particular, we will provide a model for the universal coverings of Lie tori and we show that automorphisms and derivations lift to the universal coverings. We also prove that the universal covering of a Lie ${\Lambda}$-torus of type ${\Delta}$ is again a Lie ${\Lambda}$-torus of type ${\Delta}$.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.137-148
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• 1998

We briefly discuss the Lie groups, it's nilpotency and representations of a nilpotent Lie groups. Dixmier and Kirillov proved that simply connected nilpotent Lie groups over $\mathbb{R}$ are monomial. We reformulate the above result at the Lie algebra level.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1183-1193
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• 2011

In this paper, we introduce a notion of Lie operator algebras which as a generalization of ordinary Lie algebras is an analogy of operator groups. We discuss some elementary properties of Lie operator algebras. Moreover, we also prove a decomposition theorem for Lie operator algebras.