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Nonassociative Algebras and Geometry

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http://www.hyperfract.com

Mathematics

• Hochschild DGLAS and Torsion Algebras - L. Ionescu

• Note on operadic non-associative deformations - E. Paal

• Nonassociative algebras: A Framework for Differential Geometry - L. M. Ionescu

• Methods of Non-associative Geometry in Differential Geometry - L. V. Sabinin

• On homogeneous spaces, holonomy, and non-associative algebras - A. A. Sagle

Moufang Loops/Malcev Algebras

• Simple Malcev Algebras over Fields of Characteristic Zero - A. A. Sagle

• Free Mal'tsev Algebras and Alternative Algebras - V. T. Filippov

• Moufang Loops and Malcev Algebras - P. T. Nagy

• Algebraic Mal'tsev Algebras - A. N. Grishkov

Loops in general

• C-Loops: Extensions and Constructions - Michael K. Kinyon, J. D. Philips, P. Vojtechovsky

• C-Loops: An Introduction

• On the Derivatives of Central Loops - T. G. Jaiyeola, J. O. Adeniran

• On The Universality Of Central Loops - T. G. Jaiyeola

• Smooth quasigroups and loops: Fourty-five Years of Incredible Growth - L. V. Sabinin

• Loops and Quasigroups: Aspects of Current Work and Prospects for the Future - J. D. H. Smith

 

Physics

• On Foundation of the Generalized Nambu Mechanics - L. Takhajan

Gauge Theory

• Connections and Generalized Gauged Transformations - S. Davis

• Analytic loops and gauge fields - E. K. Loginov

• On a class of gauge theories - E. K. Loginov

• On a construction of self-dual gauge fields in seven dimensions - E. K. Loginov

• Three-cocycles, Nonassociative Gauge Transforamtions and Dirac's Monopole

• A Non-associative Deformation of Yang-Mills Gauge Theory - A. Ritz, G. C. Joshi

Cocycles/Anonmalies/Monopoles

• Chern Simons Terms and Cocycles in Mathematics and Physics - R. Jackiw

• 3-Cocycles and the Operator Product Expansion - J. P. Muniain, J. Wudka

• Nonassociativity, Dirac Monopoles and Aharonov-Bohm Effect - A. I. Nesterov

• Magnetic Charge and Nonassociative Algebras - M. Gunaydin, B. Zumino

• Three-cocycles, Nonassociative Gauge Transformations and Dirac's Monopole - A. I. Nesterov

• Multi-Instantons in Higher Dimensions and Superstring Solitons - E. K. Loginov

Quantum Mechanics/QFT

Schrodinger Equation for Nonassociative Quantum Mechanics and No Go Theorem - S. Okubo

Nonassociative Quantum Mechanics via Flexible Lie Admissible Algebra - S. Okubo

Nonassociative Quantum Mechanics and Strong Correspondence Principle - S. Okubo

Nonassociative Quantum Field Theory - Liebmann

Toy Models of a Nonassociative Quantum Mechanics - v. Dzhunushaliev

QCD

• Quark confinement without a confining force - P. S. Isaac, W. P. Joyce, J. Links

• Non-Associativity on the Lattice - S. Shakirov

Gravitation

Geodesic multiplication as a Tool for Classical and Quantum Gravity - P. Kuusk, E. Paal

Operadic curvature as a tool for gravity - E. Paal

Nonassociative geometry: Towards discrete structure of spacetime - A. I. Nestrov, L. V. Sabinin

Non-associative geometry and discrete structure of spacetime - A. I. Nestrov, L. V. Sabinin

Alternative-Algebra Methods in the Special Theory of Relativity - E. K. Loginov

 

Programs

Albert's Page

LOOPS Computing with Quasigroups and Loops in GAP - G. P. Nagy, P. Vojtechovsky

 

Books

Theory of Multicodimensional (n + 1)-webs - V. V. Gol'dberg

 

Not classified (yet)

• On Anti-Commutative Algebras and General Lie Triple Systems - A. A. SAGLE

Ternary Algebras as the basis of a dynamical Theory of Subconstituents - I. Bars

emis.de/proceedings/7ICDGA ... sabinin.ps

Speciality and Deformations of Algebras - I. P. Shestakov

Decomposition of a Variety of Alternative Algebras into a Subvariety Product - V. T. Filippov

Local Algebras of a Multidimensional Three-Web - M. A. Akivis

Binary Lie Algebras of Small Dimensions - E. N. Kuzmin

Classification Of Flexible Composition Algebras 2 - S. Okubo

Classification Of Flexible Composition Algebras 1 - S. Okubo

Dimension and Classification of General Composition Algebras - S. Okubo

Construction of Nonassociative Algebras from Representation Modules of Simple Lie Algebras - S. Okubo

Local Ternary Quasigroups associated with a 4-Web of Multidimensional Surfaces - V. V. Gol'dberg

Co-Addition for free non-associative Algebras and the Hausdorff Series - L. Gerritzen, R. Holtkamp

 

Related topics: Quaternions, Octonions, Sedenion, Geometric Algebra, Hypercomplex Numbers