Algebra Environments

Concepts, Themes, and Use Cases
Erscheinungsjahr 2027
ISBN: 978-3-032-46530-6
Verlag: Birkhäuser

Buch, Englisch, Format (B × H): 168 mm x 240 mm

Reihe: Frontiers in Mathematics

This monograph introduces algebra environments as a single unifying framework that connects operator algebras, differential geometry, Clifford analysis, spectral theory, and harmonic analysis. By studying algebra environments and their structure manifolds, the book reveals deep geometric and analytic connections across fields which are traditionally studied in isolation. The book develops new tools such as symbol and conjugation operators, Banach manifold structures, geodesics, and holomorphic projection techniques, which are then applied to problems ranging from projective group representations to Dirac-type operators and spin geometry.

Rich with original insights and multidisciplinary links, this book opens new avenues for research and offers a rich toolkit for mathematicians working in analysis, geometry, and operator theory.

Zielgruppe

Research

Autoren/Hrsg.

Martin, Mircea

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Chapter 1. Algebra Environments – Algebraic Approach.- Chapter 2. Hom Environments and Geometric Structures on Vector Bundles.- Chapter 3. Algebra Environments – Topological Approach.- Chapter 4. Projective Compact Group Representations.- Chapter 5. Deconstructing Euclidean Dirac and Cauchy–Riemann Operators.- Chapter 6. Holomorphic Spectral Theory.- Chapter 7. Spin Operator Theory.

Über Autor(innen)

Mircea Martin is a retired emeritus professor of mathematics at Baker University, USA. His primary research interests lie in functional analysis, operator theory, and Clifford analysis. His work explores advanced topics such as Euclidean Dirac operators, non-commutative algebraic structures, and geometric methods in analysis, with applications to harmonic analysis and spectral theory. He has contributed to the development of theoretical frameworks connecting algebra, geometry, and differential analysis, particularly through his studies of algebra environments and operator systems.