Advances in Applied Clifford Algebras最新文献

The Double Dihedral Dunkl Total Angular Momentum Algebra 双二面体Dunkl总角动量代数

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-05-07 DOI: 10.1007/s00006-026-01441-x

Marcelo De Martino, Alexis Langlois-Rémillard, Roy Oste

引用次数: 0

Complex Structure-Preserving Algorithm for LU Decomposition of Dual Quaternion Matrices and Its Application 对偶四元数矩阵LU分解的复结构保持算法及其应用

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-04-28 DOI: 10.1007/s00006-026-01446-6

Xiaochen Liu, Ying Li, Ruyu Tao, Jianhua Sun

{"title":"Complex Structure-Preserving Algorithm for LU Decomposition of Dual Quaternion Matrices and Its Application","authors":"Xiaochen Liu, Ying Li, Ruyu Tao, Jianhua Sun","doi":"10.1007/s00006-026-01446-6","DOIUrl":"10.1007/s00006-026-01446-6","url":null,"abstract":"<div>Dual quaternion has a wide range of applications in various fields, and the study of its matrix theory has become a hot topic in recent years. In the theoretical study of dual quaternion matrices, the LU decomposition plays an important role. However, due to the non-commutativity of dual quaternions, the calculation of LU decomposition becomes difficult. In this paper, by means of the quaternion representation of the dual quaternion matrices given by semi-tensor product of matrices and the complex representation of the quaternion matrices, we give the complex representation of the dual quaternion matrices and its properties. The complex representation we proposed greatly facilitates the simplification of computational processes. And using these properties, we propose a fast and efficient complex structure-preserving algorithm for LU decomposition of dual quaternion matrices. The algorithm avoids the complexity of dual quaternion operations (essentially, quaternion operations). In order to ensure the stability of the algorithm, we further give a partial pivoting dual quaternion LU decomposition algorithm. Based on LU decomposition, we also present a complex structure-preserving algorithm for (LDL^H) decomposition of dual quaternion Hermitian matrices. In addition, we illustrate the effectiveness of the complex structure-preserving algorithms through numerical experiments. Finally, we give the application of dual quaternion matrix LU decomposition in color image authentication and kinematic linear equations.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147756100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Limiting Sobolev Inequalities for k-Cauchy–Fueter Complex k-Cauchy-Fueter复合体的极限Sobolev不等式

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-04-27 DOI: 10.1007/s00006-026-01443-9

Xin Luo, Sihan Ning

引用次数: 0

Extensions of Jacobson’s Lemma and Cline’s formula in the Quaternionic Setting Jacobson引理和Cline公式在四元数情况下的扩展

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-04-11 DOI: 10.1007/s00006-026-01440-y

Aziz Blali, Abdellah El Allaoui, Abdelkhalek El Amrani

引用次数: 0

Riemann–Hilbert Problems for Biaxially Symmetric Null Solutions to Iterated Perturbed Dirac Equations in (mathbb {R}^{n}) 中迭代扰动Dirac方程双轴对称零解的Riemann-Hilbert问题 $$mathbb {R}^{n}$$

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-04-06 DOI: 10.1007/s00006-026-01444-8

Dian Zuo, Min Ku, Fuli He

引用次数: 0

Fourier Transform on Cayley–Dickson Algebras Cayley-Dickson代数上的傅里叶变换

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-02-20 DOI: 10.1007/s00006-026-01439-5

Shihao Fan, Guangbin Ren

{"title":"Fourier Transform on Cayley–Dickson Algebras","authors":"Shihao Fan, Guangbin Ren","doi":"10.1007/s00006-026-01439-5","DOIUrl":"10.1007/s00006-026-01439-5","url":null,"abstract":"<div>We introduce the Cayley–Dickson Fourier transform (CDFT), a novel framework for harmonic analysis of functions valued in the non-associative Cayley–Dickson algebras ( mathcal {C}_m ). The central challenge lies in the failure of associativity and alternativity for ( m geqslant 4 ), which obstructs classical Fourier analytic methods. To overcome this, we develop a two-stage approach: first, we construct the transform on real-valued Schwartz-type spaces, establishing continuity, inversion, and isometric properties; second, we extend the theory to fully ( mathcal {C}_m )-valued functions by leveraging intrinsic algebraic structures, such as slice-wise multiplicativity and weak commutativity. Key innovations include a modified duality between differentiation and multiplication, governed by twisted sign involutions that precisely compensate for non-associative distortions, and a restricted convolution theorem for Gaussian-type functions that exploits the real scalar structure of their transforms. We prove that the CDFT admits an explicit inverse via symmetrization over coordinate reflections, acts isometrically on ( L^2(mathbb {R}^m, mathcal {C}_m) ), and exhibits a period-four symmetry that generalizes classical Fourier periodicity. These results collectively establish the CDFT as a rigorous and structurally faithful extension of Fourier analysis to the full Cayley–Dickson hierarchy.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bicomplex Polyholomorphic Bergman Spaces Associated with a Bicomplex Magnetic Laplacian on the Discus 铁饼上与双复磁拉普拉斯算子相关的双复多全纯Bergman空间

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-02-14 DOI: 10.1007/s00006-026-01438-6

Issame Ahizoune, Aiad Elgourari, Allal Ghanmi

引用次数: 0

Construction of Exceptional Lie Algebra G2 and Non-associative Algebras Using Clifford Algebra 利用Clifford代数构造例外李代数G2和非结合代数

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2026-02-14 DOI: 10.1007/s00006-025-01423-5

G. P. Wilmot

引用次数: 0

Monoids of Compatible Bilinear Forms in Relation to Lipschitz Monoids 与Lipschitz一元群相关的相容双线性型一元群