Exotic Algebraic and Geometric Structures in Theoretical Physics

Steven Duplij
University of Münster, Germany

Series: Contemporary Fundamental Physics
BISAC: SCI040000

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This collection presents original mathematical ideas and unusual constructions in theoretical physics. They were developed locally at Kharkov University, Ukraine, and now can be presented to Western readers. The subjects are broad and cover an array of ideas, from regular generalization of supermanifolds and category theory, coalgebras, the Yang-Baxter equation and Hopf algebras, to nontrivial aspects of nilpotent mechanics, fermionic gravity and multigravity, the constraintless Hamiltonian approach to singular theories, and the application of polyadic structures to representation theory and quantum groups. The book can attract researchers and post-graduate students who are interested in new developments and methods in modern theoretical physics and related directions in mathematics.

Preface

Acknowledgements

Chapter 1. Higher Regularity and Obstructed Categories

Chapter 2. Semisupermanifolds and Regularization

Chapter 3. Obstructed Categories and Regular Graded Algebras

Chapter 4. Toposes and Categories in Quantum Theory and Gravity

Chapter 5. Braid Semistatistics and Doubly Regular R-Matrix

Chapter 6. Weak Hopf Algebras and New Solutions of Yang-Baxter Equation

Chapter 7. Complete Uq(sl2)-symmetries On Quantum Plane

Chapter 8. Coderivations and Codifferential Calculi on Finite Groups

Chapter 9. Semigroups of Supermatrices And Idempotent Superoperators

Chapter 10. Supersymmetry and Nilpotent Mechanics

Chapter 11. Constraintless Hamiltonian Formalism and New Brackets

Chapter 12. Generalized Interaction and Coincidence Limit in Multigravity

Chapter 13. Fermionic Lineal Gravity

Chapter 14. Polyadic Algebraic Structures and Their Representations

Chapter 15. Ternary Hopf Algebras and Quantum Groups

Contributors

Bibliography

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