• 충청수학회지
• /
• 제23권2호
• /
• pp.363-368
• /
• 2010

In this paper we construct a subalgebra $L_8$ of $M_8({\mathbb{R}})$ which is a generalization of the algebra of quaternions. Moreover we prove that the algebra $L_8$ is the real Clifford algebra $Cl_3$, and so $L_8$ is a matrix representation of Clifford algebra $Cl_3$.

• 충청수학회지
• /
• 제27권4호
• /
• pp.571-579
• /
• 2014

In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{\ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.

• 대한수학회논문집
• /
• 제35권2호
• /
• pp.487-497
• /
• 2020

In this paper, we establish a complex matrix representation of the Clifford algebra Cℓ_p,q. The size of our representation is significantly smaller than the size of the elements in L_p,q(ℝ). Additionally, we give detailed information about the spectrum of the constructed matrix representation.

• 대한수학회지
• /
• 제34권1호
• /
• pp.167-179
• /
• 1997

In the study of a manifold M, the exterior algebra $\Lambda^* M$ plays an important role. In fact, the de Rham cohomology theory gives many informations of a manifold. Another important object in the study of a manifold is its Clifford algebra (Cl(M), generated by the tangent space.

• Korean Journal of Mathematics
• /
• 제30권3호
• /
• pp.491-502
• /
• 2022

In this paper we investigate some sufficient conditions to guarantee the existence and uniqueness of Stepanov-like weighted pseudo almost periodic solutions of cellular neural networks on Clifford algebra for non-automomous cellular neural networks with multi-proportional delays. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• 대한수학회보
• /
• 제35권4호
• /
• pp.669-681
• /
• 1998

In this paper, we prove that on the complete Kahler manifold, if ${\rho}(x){\geq}-\frac{1}{2}{\lambda}_0$ and either ${\rho}(x_0)>-\frac{1}{2}{lambda}_0$ at some point $x_0$ or Vol(M)=${\infty}$, then the Clifford $L^2$ cohomology group $L^2{\mathcal H}^{\ast}(M,S)$ is trivial, where $\rho(x)$ is the least eigenvalue of ${\mathcal R}_x + \bar{{\mathcal R}}(x)\;and\;{\lambda}_0$ is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.767-781
• /
• 1996

We shall prove some vanishing theorems for the tranversal Dirac operators on $K\ddot{a}$hler foliations.

• 대한수학회보
• /
• 제55권5호
• /
• pp.1483-1490
• /
• 2018

In this note, it is proven that the slice Bergman kernels for some axially symmetric slice domains are zero-free by a simple method.

• 대한수학회보
• /
• 제60권2호
• /
• pp.307-313
• /
• 2023

In this paper, we study the n-dimensional Möbius transformation. We obtain several conjugacy invariants and give a conjugacy classification for n-dimensional Möbius transformation.

• 대한수학회지
• /
• 제61권1호
• /
• pp.109-132
• /
• 2024

The Clifford algebra of a direct sum of real quadratic spaces appears as the superalgebra tensor product of the Clifford algebras of the summands. The purpose of the current paper is to present a purely settheoretical version of the superalgebra tensor product which will be applicable equally to groups or to their non-associative analogues - quasigroups and loops. Our work is part of a project to make supersymmetry an effective tool for the study of combinatorial structures. Starting from group and quasigroup structures on four-element supersets, our superproduct unifies the construction of the eight-element quaternion and dihedral groups, further leading to a loop structure which hybridizes the two groups. All three of these loops share the same character table.