• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.615-625
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• 2018

In this paper, we discuss the connection between the 5-dimensional complex Lie algebra ${\mathcal{K}} _5$ and Special functions. We construct certain two variable models of the irreducible representations of ${\mathcal{K}}_5$. We also use an Euler type integral transformation to obtain the new transformed models, in which the basis function appears as $_2F_1$. Further, we utilize these models to get some generating functions and recurrence relations.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.385-397
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• 2022

Let (M, [ , ]) be a finite dimensional Malcev algebra over an algebraically closed field 𝔽 of characteristic 0. We first prove that, (M, [ , ]) (with [M, M] ≠ 0) is simple if and only if ind(M) = 1 (i.e., M admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.191-200
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• 1995

Simple Lie albegras over algebraically closed field with characteristic p > 7 were classified by H. Strade and R. L. Wilson in 1991 [7]. All modular representations of simple Lie algebras, however, are not classified although some restricted modular representations have been done earlier by Curtis and Steinberg. In connection with this, we would like to decompose basic $sp_4$(F)-modules $sl_4$-(F) and $gl_4$(F) over nonzero characteristic by way of characteristic zero case.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.887-902
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• 2023

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y²] + [x², f(y)] on a 𝜌-complete convex modular *-algebra χ_𝜌 by using ∆₂-condition via convex modular 𝜌.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.443-456
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• 2005

Let G be a Lie group, let L(G) be its Lie algebra, and let exp : $L(G){\rightarrow}G$ denote the exponential mapping. For $S{\subseteq}G$, we define the tangent set of S by $L(S)\;=\;\{X\;{\in}\;L(G)\;:\;exp(tX)\;\in\;S\;for\;all\;t\;{\geq}\;0\}$. We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebras

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.45-52
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• 2006

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.

• International Journal of Internet, Broadcasting and Communication
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• v.9 no.3
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• pp.35-43
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• 2017

In 2013, Lee-Lie proposed secure smart card based authentication scheme of Zhu's authentication for TMIS which is secure against the various attacks and efficient password change. In this paper, we discuss the security of Lee-Lie's smart card-based authentication scheme, and we have shown that Lee-Lie's authentication scheme is still insecure against the various attacks. Also, we proposed the improved scheme to overcome these security problems of Lee-Lie's authentication scheme, even if the secret information stored in the smart card is revealed. As a result, we can see that the improved smart card based user authentication scheme for TMIS is secure against the insider attack, the password guessing attack, the user impersonation attack, the server masquerading attack, the session key generation attack and provides mutual authentication between the user and the telecare system.

• Korean Journal of Child Studies
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• v.35 no.4
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• pp.167-177
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• 2014

The study examined the influences of age, empathy and perspective taking ability on altruistic lying in 5 and 6 year old children. Eighty three children answered a question as to whether a protagonist would lie after listening to three vignettes involving altruistic lies. Korean versions of the Affective Situation Test(AST) and cognitive perspective taking task were used to measure children's empathy and perspective taking respectively. The results of the study showed that there were significant differences in altruistic lying by age. Altruistic lie by children was positively related with their age, empathy and perspective taking ability. In particular, age and perspective taking ability are important factors influencing children's altruistic lie in young children in Korea.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.427-442
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• 2014

A previous work gave a combinatorial description of the crystal B(${\infty}$), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(${\lambda}$), in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of B(${\lambda}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.5-16
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• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.