Clifford Algebras

1. Front Matter

   Pages 1-18

   PDF

2. Models and Representations

   • Daniel Klawitter

   Pages 5-99

3. Chain Geometry over Clifford Algebras

   • Daniel Klawitter

   Pages 101-180

4. Kinematic Mappings for Spin Groups

   • Daniel Klawitter

   Pages 181-199

5. Back Matter

   Pages 201-216

   PDF

After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework.

• Cayley-Klein geometries
• Clifford algebra model
• Euclidean displacements
• Euclidean geometry
• hyperquadrics
• kinematic mappings

“Clifford and geometrical algebras are powerful calculation tools that unify geometric concepts from different algebraic structures built over time … . In this book, the author makes use of this powerful mathematical tool, specifically Clifford algebras and their Spin and Pin groups, to unify different kinematic mappings … . I find this book a great accomplishment and definitely recommend it.” (Eduardo A. Notte Cuello, Mathematical Reviews, May, 2016)

• TU Dresden Institut für Geometrie, Dresden, Germany

  Daniel Klawitter

Daniel Klawitter is a scientific assistant at the Institute of Geometry at the Technical University of Dresden, Germany.

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