图书简介
Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy.Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science.The book is laid out in twelve main topics where we can find relevant works from distinguished experts.Key FeaturesFurther developments and related researches of Prof Oziewicz’s influential and original scientific researches in various areas of science, which are followed by a relatively large circle of peopleContribution by many researchers of good academic standing in the current research in applications of category theory to mathematics (Geometry, topology, etc.), sciences, computing and humanities, which are of high interestNew developments in knot theory in the category theory contexts, and relations to other sciences and humanities
Zbigniew Oziewicz’s Biographical Notes; Einstein’s Composition of Velocities and Symmetric Spaces of E Cartan; Didactic Experiences with the Moodle for Critical and Creative Thinking; A Construction for Clifford Algebras; Exponential of Endomorphism with Minimal Polynomial; Mathematics and Physical Meaning in Relativistic Quantum Mechanics; Composition of Relativistic Velocities: Algebraic Loop Deformation and Geometry; Evolution Equations of Relativistic Dynamics; Relative Binary and Ternary 4D velocities in SR: I. Covariant Lorentz Transformation; The Space-Time Theories Exploratorium; Classical Relativity and Quantum Relativity Versus Special Relativity; Quantum Calculi: Differential Forms and Vector Fields; Zbigniew Oziewicz’s Differential Calulus; On Binary Lie Algebras with Identities; Kepler Problem, Lorentz Transformation, and Jordan Algebra; On The Leavitt Path Algebras of a Class of Random Graphs; Homology of Small Categories; The Golden Ratio, Variational Principles, Cyclic and Wave Phenomena and Quanta; Some Categories of Alexandroff Spaces; Parametric Hopf Adjunctions and Monads; Visible and Invisible States; SU(n) and Quantum SU(n) Symmetries in Physical Systems; Projective View on Motion Groups II: A Quest for Rational Geometries; Spheroidal Quaternions and Symmetries; Special Affine Quaternion Domain Fourier Transform; Vortices and TQFTs; On Negative-Energy 4-Spinors and Masses in the Dirac Equation; Yang–Mills–Scalar–Matter Fields in the Two-Point Space; Representation of the Anomalous Magnetic Moment of The Muons; The Standard Model of Elementary Particle Physics; Superdense Coding and Communication Protocols; Computable Isomorphism Problem; On Generating Function for Quantum Hyperbolic Planes; Weak Gravitational Fields in the Geometric Algebra Approach
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