Classical Clifford Algebras

Part I. Motivation: On the Quaternions H. 1. Introduction of Part I. 2. On the Quaternions H. 3. Spectral Analysis on H Under (C2; ?). 4. 4. On Noncommutative Field H Under (C2; ?). 5. Free-Probabilistic Data Induced by H. Part II. On the Classical Clifford Algebras. 6. Introduction of Part II. 7. Classical Clifford Algebras. 8. Free Probability on the Clifford-Group C*-Probability Space (MG ; T). 9. Free Probability on Certain Sub-Structures of (MG; T). Part III. The Clifford Group G and the Semicircular Law. 10. Introduction of Part III. 11. On the Tensor Product C*-Probability C-Spaces (MG O A; T O ?). 12. Deformed Semicircular Laws on (MG O A; T O ?). 13. Applications. Part IV. Representations of the Clifford Algebra C. 14. Introduction of Part IV. 15. The Clifford Algebra C Embedded in the CG C*-Algebra MG. 16. On the R-Banach *-Algebra C. 17. R-Adjointable-Operator-Theoretic Properties on C. 18. Discussions.