2014, Mathematical surveys and monographs, ISBN 9781470417109, Volume 200, vii, 240

Differential equations, Elliptic | Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) | Nonassociative rings and algebras -- General nonassociative rings -- Division algebras | Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries | Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations | Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces | Jordan algebras | Nonassociative rings

Book

2017, Graduate studies in mathematics, ISBN 9781470437701, Volume 183, xxi, 637 pages

Algebraic geometry -- (Co)homology theory -- Étale and other Grothendieck topologies and (co)homologies | Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.) | Commutative algebra -- General commutative ring theory -- Ideals; multiplicative ideal theory | Separable algebras | Algebraic geometry -- Local theory -- Local structure of morphisms: Étale, flat, etc | Commutative algebra -- Ring extensions and related topics -- Galois theory | Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | Commutative algebra -- Ring extensions and related topics -- Étale and flat extensions; Henselization; Artin approximation | Associative rings | Associative rings and algebras -- Instructional exposition (textbooks, tutorial papers, etc.) | Commutative algebra -- Theory of modules and ideals -- Class groups

Book

2014, Princeton series in applied mathematics, ISBN 0691161852, xii, 363

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important...

Quaternions | Algebras, Linear | Mathematics | Algebra | General, Technology & Engineering | Complex Analysis, PBF, PBK, PBKD, UY, PH, TBC | Calculus, Science | Engineering (General), Mathematics | Computer Science, Mathematics | Physics | Linear, Computers | Quaternions Textbooks | Technology | Textbooks

Quaternions | Algebras, Linear | Mathematics | Algebra | General, Technology & Engineering | Complex Analysis, PBF, PBK, PBKD, UY, PH, TBC | Calculus, Science | Engineering (General), Mathematics | Computer Science, Mathematics | Physics | Linear, Computers | Quaternions Textbooks | Technology | Textbooks

Book

2017, University Lecture Series, ISBN 147044187X, Volume 69, 151 pages

Book

IEEE Transactions on Signal Processing, ISSN 1053-587X, 07/2019, Volume 67, Issue 14, pp. 3649 - 3662

This paper reformulates adaptive filters (AFs) in the framework of geometric algebra (GA), developing a complete study of the resulting geometric-algebra...

Three-dimensional displays | Quaternions | geometric algebra | Adaptive filtering | Cost function | Calculus | Matrices | Standards

Three-dimensional displays | Quaternions | geometric algebra | Adaptive filtering | Cost function | Calculus | Matrices | Standards

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 06/2017, Volume 99, pp. 32 - 35

In this paper, we introduce h(x) – Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K(K=R,C). These polynomials generalize...

h(x) - Fibonacci quaternion polynomials | h(x) - Fibonacci octonion polynomials | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | NUMBERS | PHYSICS, MULTIDISCIPLINARY | SPLIT FIBONACCI | PHYSICS, MATHEMATICAL | OCTONIONS | QUATERNIONS | Analysis | Algebra | Computer science

h(x) - Fibonacci quaternion polynomials | h(x) - Fibonacci octonion polynomials | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | NUMBERS | PHYSICS, MULTIDISCIPLINARY | SPLIT FIBONACCI | PHYSICS, MATHEMATICAL | OCTONIONS | QUATERNIONS | Analysis | Algebra | Computer science

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 01/2018, Volume 1926, Issue 1

In this study, we define the elliptic biquaternions and construct the algebra of elliptic biquaternions over the elliptic number field. Also we give basic...

Quaternions | Algebra

Quaternions | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2018, Volume 505, pp. 490 - 558

A finite-dimensional algebra A over an algebraically closed field K is called periodic if it is periodic under the action of the syzygy operator in the...

Periodic algebra | Surface algebra | Tame algebra | Syzygy | Self-injective algebra | STABLE EQUIVALENCE | BISERIAL ALGEBRAS | DEFORMED PREPROJECTIVE ALGEBRAS | GENERALIZED DYNKIN TYPE | SYMMETRIC ALGEBRAS | QUATERNION DEFECT-GROUPS | MATHEMATICS | POLYNOMIAL-GROWTH | CLUSTER ALGEBRAS | HOCHSCHILD COHOMOLOGY | SELF-INJECTIVE ALGEBRAS

Periodic algebra | Surface algebra | Tame algebra | Syzygy | Self-injective algebra | STABLE EQUIVALENCE | BISERIAL ALGEBRAS | DEFORMED PREPROJECTIVE ALGEBRAS | GENERALIZED DYNKIN TYPE | SYMMETRIC ALGEBRAS | QUATERNION DEFECT-GROUPS | MATHEMATICS | POLYNOMIAL-GROWTH | CLUSTER ALGEBRAS | HOCHSCHILD COHOMOLOGY | SELF-INJECTIVE ALGEBRAS

Journal Article

Annals of Physics, ISSN 0003-4916, 10/2017, Volume 385, pp. 180 - 213

Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are...

Quantization | Displacement operator | Lie algebra | Quaternion | Coherent states | PHYSICS, MULTIDISCIPLINARY | QUANTUM-MECHANICS | Algebra | Computer science | HILBERT SPACE | UNCERTAINTY PRINCIPLE | HARMONIC OSCILLATORS | POSITION OPERATORS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | LIE GROUPS

Quantization | Displacement operator | Lie algebra | Quaternion | Coherent states | PHYSICS, MULTIDISCIPLINARY | QUANTUM-MECHANICS | Algebra | Computer science | HILBERT SPACE | UNCERTAINTY PRINCIPLE | HARMONIC OSCILLATORS | POSITION OPERATORS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | LIE GROUPS

Journal Article

Journal of Algebra, ISSN 0021-8693, 04/2016, Volume 451, pp. 145 - 165

We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the...

Nonassociative quaternion algebra | Nonassociative cyclic algebra | Tensor product | Division algebra | Cyclic algebra | Secondary | Primary | MATHEMATICS | DIVISION | Algebra

Nonassociative quaternion algebra | Nonassociative cyclic algebra | Tensor product | Division algebra | Cyclic algebra | Secondary | Primary | MATHEMATICS | DIVISION | Algebra

Journal Article

Proceedings of the IEEE, ISSN 0018-9219, 09/2014, Volume 102, Issue 9, pp. 1340 - 1363

In this paper, we explicate the suggested benefits of Clifford's geometric algebra (GA) when applied to the field of electrical engineering. Engineers are...

Geometry | Algebra | Quaternions | Magnetic separation | electromagnetism | geometric algebra (GA) | relativity | Mathematics | Clifford algebra | Maxwell's equations | Doppler effect | Electric fields | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Learning curves | Problem solving | Electronics | Representations | Cases (containers)

Geometry | Algebra | Quaternions | Magnetic separation | electromagnetism | geometric algebra (GA) | relativity | Mathematics | Clifford algebra | Maxwell's equations | Doppler effect | Electric fields | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Learning curves | Problem solving | Electronics | Representations | Cases (containers)

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2018, Volume 51, Issue 1, pp. 51 - 88

We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These...

Periodic algebra | Tame algebra | Weighted surface algebra | Biserial weighted surface algebra | Quiver combinatorics | Brauer graph algebra | Symmetric algebra | Special biserial algebra | HECKE ALGEBRAS | MATHEMATICS | REPRESENTATION TYPE | MODULES | BLOCKS

Periodic algebra | Tame algebra | Weighted surface algebra | Biserial weighted surface algebra | Quiver combinatorics | Brauer graph algebra | Symmetric algebra | Special biserial algebra | HECKE ALGEBRAS | MATHEMATICS | REPRESENTATION TYPE | MODULES | BLOCKS

Journal Article

IEEE Transactions on Robotics, ISSN 1552-3098, 10/2014, Volume 30, Issue 5, pp. 1037 - 1048

Dual quaternions give a neat and succinct way to encapsulate both translations and rotations into a unified representation that can easily be concatenated and...

spatial kinematics | Quaternions | Robot kinematics | Biquaternions | Cayley factorization | Vectors | Matrix decomposition | double quaternions | dual quaternions | quaternions | ROBOTICS | DISPLACEMENTS | VECTORS | Usage | Approximation theory | Matrices | Analysis | Robots | Kinematics | Encapsulation | Construction | Approximation | Transformations | Translations | Three dimensional | Aproximació, Teoria de l | Cinemàtica | Matrius (Matemàtica) | Spatial kinematics | Dual quaternions | Informàtica | Robòtica | Double quaternions | Àrees temàtiques de la UPC

spatial kinematics | Quaternions | Robot kinematics | Biquaternions | Cayley factorization | Vectors | Matrix decomposition | double quaternions | dual quaternions | quaternions | ROBOTICS | DISPLACEMENTS | VECTORS | Usage | Approximation theory | Matrices | Analysis | Robots | Kinematics | Encapsulation | Construction | Approximation | Transformations | Translations | Three dimensional | Aproximació, Teoria de l | Cinemàtica | Matrius (Matemàtica) | Spatial kinematics | Dual quaternions | Informàtica | Robòtica | Double quaternions | Àrees temàtiques de la UPC

Journal Article

Annals of Science, ISSN 0003-3790, 01/2016, Volume 73, Issue 1, pp. 40 - 67

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's...

CAMBRIDGE | PEACOCK | CALCULUS | HISTORY & PHILOSOPHY OF SCIENCE | TREATISE | PURE TIME | HAMILTON | HISTORY | Mathematics - history | History, 19th Century | United Kingdom | Euclidean space | Algebra | Arbiters | British | Euclidean geometry | Quaternions | Mathematical analysis | Documents | Radicals

CAMBRIDGE | PEACOCK | CALCULUS | HISTORY & PHILOSOPHY OF SCIENCE | TREATISE | PURE TIME | HAMILTON | HISTORY | Mathematics - history | History, 19th Century | United Kingdom | Euclidean space | Algebra | Arbiters | British | Euclidean geometry | Quaternions | Mathematical analysis | Documents | Radicals

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 5/2017, Volume 352, Issue 1, pp. 95 - 133

We define a planar para algebra, which arises naturally from combining planar algebras with the idea of $${\mathbb{Z}_{N}}$$ Z N para symmetry in physics. A...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | SUBFACTORS | NETS | MODELS | MODULAR INVARIANTS | PHYSICS, MATHEMATICAL | Atoms | Algebra

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | SUBFACTORS | NETS | MODELS | MODULAR INVARIANTS | PHYSICS, MATHEMATICAL | Atoms | Algebra

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 06/2013, Volume 23, Issue 2, pp. 377 - 404

We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed...

geometry | engineering | Hypercomplex algebra | hypercomplex analysis | science | applications | MATHEMATICS, APPLIED | FOURIER-TRANSFORM | PHYSICS, MATHEMATICAL | QUATERNION | Equipment and supplies | Electromagnetism | Algebra | Image processing | Electronics in navigation

geometry | engineering | Hypercomplex algebra | hypercomplex analysis | science | applications | MATHEMATICS, APPLIED | FOURIER-TRANSFORM | PHYSICS, MATHEMATICAL | QUATERNION | Equipment and supplies | Electromagnetism | Algebra | Image processing | Electronics in navigation

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 1036 - 1116

We introduce and study the algebras of generalized quaternion type, being natural generalizations of algebras which occurred in the study of blocks of group...

Periodic algebra | Symmetric algebra | Tame algebra | Cohen-Macaulay module | Generalized quaternion type | Weighted surface algebra | QUIVERS | POTENTIALS | MATHEMATICS | FINITE | BLOCKS | PERIODIC RESOLUTIONS | CATEGORY | SELF-INJECTIVE ALGEBRAS

Periodic algebra | Symmetric algebra | Tame algebra | Cohen-Macaulay module | Generalized quaternion type | Weighted surface algebra | QUIVERS | POTENTIALS | MATHEMATICS | FINITE | BLOCKS | PERIODIC RESOLUTIONS | CATEGORY | SELF-INJECTIVE ALGEBRAS

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2019, Volume 22, Issue 2, pp. 387 - 406

We introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The...

16G60 | Periodic algebra | Associative Rings and Algebras | Tame algebra | Syzygy | Non-associative Rings and Algebras | 16D50 | Commutative Rings and Algebras | Symmetric algebra | Mathematics | 16S80 | 16G20 | MATHEMATICS | TAME | FINITE | SELF-INJECTIVE ALGEBRAS | Computer science | Algebra

16G60 | Periodic algebra | Associative Rings and Algebras | Tame algebra | Syzygy | Non-associative Rings and Algebras | 16D50 | Commutative Rings and Algebras | Symmetric algebra | Mathematics | 16S80 | 16G20 | MATHEMATICS | TAME | FINITE | SELF-INJECTIVE ALGEBRAS | Computer science | Algebra

Journal Article

Lettera Matematica, ISSN 2281-6917, 8/2017, Volume 5, Issue 2, pp. 75 - 80

This is a very brief overview of some of the main ideas of algebra through history, from the decomposition of a binomial identity, to the degree of a complex...

Mathematical Methods in Physics | History of Science | Algebra | Quaternions | Theoretical, Mathematical and Computational Physics | Lie algebras | Mathematics, general | Mathematics | History of Mathematical Sciences | Applications of Mathematics | Number theory

Mathematical Methods in Physics | History of Science | Algebra | Quaternions | Theoretical, Mathematical and Computational Physics | Lie algebras | Mathematics, general | Mathematics | History of Mathematical Sciences | Applications of Mathematics | Number theory

Journal Article

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