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, 2021 This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature.
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Serre weights for quaternion algebras [PDF]
Compositio Mathematica, 2011 AbstractWe study the possible weights of an irreducible two-dimensional mod p representation of ${\rm Gal}(\overline {F}/F)$ which is modular in the sense that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field.
Gee, T., Savitt, D.
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Angular Momentum, Quaternion, Octonion, and Lie-Super Algebra osp(1,2) [PDF]
, 1997 We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three.
Okubo, Susumu
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Linear Algebra and its Applications, 1984 AbstractLie algebras which are isomorphic to central quotients of quaternion division algebras are investigated.
Rolf Farnsteiner, Rolf Farnsteiner
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IEEE Access, 2023 The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model
Eduardo Bayro-Corrochano +2 more
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Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4 [PDF]
, 2007 Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a p-adic ring.
Broué +6 more
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Quaternions and Clifford Algebras
, 2022 Quaternions are a type of hypercomplex numbers. Unit quaternions, which describe rotations, were called versors by Hamilton. The concept of versor can be generalized as the product of invertible vectors in the Clifford algebra. Clifford algebras are also named geometric algebras, when referring to the subset of nondegenerate Clifford algebras ...
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Enabling quaternion derivatives: the generalized HR calculus [PDF]
Royal Society Open Science, 2015 Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective
Dongpo Xu +3 more
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A Convolution Theorem Related to Quaternion Linear Canonical Transform
Abstract and Applied Analysis, 2019 We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain
Mawardi Bahri, Ryuichi Ashino
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Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System
International Journal of Applied Mathematics and Computer Science, 2023 This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen ...
Kitowski Zygmunt +2 more
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