Spatial Algebras: Algebraic Foundations, Spectral Reconstruction, and Applications - Softcover

Cāmara, Kleber Soares

Softcover

ISBN 10: 6502363733 ISBN 13: 9786502363737

Publisher: Ed. do Autor, 2026

Synopsis

Spatial Algebras develops a new algebraic framework obtained by extending the complex plane with real idempotent directions while preserving the identity of each channel. The resulting structures are commutative and have an identity element, but they are generally nonassociative. Rather than treating nonassociativity merely as a defect, the book shows how the associator can be used to reconstruct spatial information lost under complex projection.

Beginning with the necessary foundations, the text first develops finite-dimensional spatial algebras and then extends the theory to infinite-dimensional families built over classical sequence spaces. Topics include multiplication operators, spectral theory, resolvents, functional calculus, coupled spectral representations, associator reconstruction, and Hilbertian geometry.

The theory is subsequently transported to bundles and dynamical systems, with discussions of projectors, connections, transfer between channels, curvature, symmetries, and bifurcation. The final part presents two advanced applications: Multichannel Spectral Geometry and a positive realization of Kaluza-Klein channels.

Designed for readers with an undergraduate degree in mathematics, the book is self-contained and requires no previous study of nonassociative algebras. Definitions are supported by conceptual preparation, detailed proofs, examples, counterexamples, graded exercises, and answers or hints. Clear warnings distinguish established results from open directions and delimit the mathematical scope of the physical applications.

This volume will be of interest to students, researchers, and instructors working in algebra, functional analysis, operator theory, spectral theory, differential geometry, and mathematical physics.

About this title

About the Author

Kleber Soares Cāmara holds a PhD in Mathematics from the Federal University of Paraķba and is a professor at the Federal Rural University of the Semi-Arid Region (UFERSA), Brazil. His academic work focuses on mathematical analysis, operator theory, spectral theory, nonassociative algebras, and their applications. He has taught undergraduate and graduate mathematics since 2012.

Edition details

• Publisher: Ed. do Autor
• Publication date: 2026
• Language: English
• ISBN 10: 6502363733
• ISBN 13: 9786502363737
• Binding: Paperback
• Number of pages: 626