1st Edition

Classical Clifford Algebras Operator-Algebraic and Free-Probabilistic Approaches

By Ilwoo Cho Copyright 2024
    134 Pages
    by Chapman & Hall

    Classical Clifford Algebras: Operator-Algebraic and Free-Probabilistic Approaches offers novel insights through operator-algebraic and free-probabilistic models. By employing these innovative methods, the author sheds new light on the intrinsic connections between Clifford algebras and various mathematical domains. This monograph should be an essential addition to the library of any researchers interested in Clifford Algebras or Algebraic Geometry more widely.


    • Includes multiple examples and applications
    • Suitable for postgraduates and researchers working in Algebraic Geometry
    • Takes an innovative approach to a well-established topic

    Part I. Motivation: On the Quaternions H. 1. Introduction of Part I. 2. On the Quaternions H. 3. Spectral Analysis on H Under (C2; π). 4. 4. On Noncommutative Field H Under (C2; π). 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 (MØ A; T Ø ⴏ). 12. Deformed Semicircular Laws on (MØ A; T Ø ⴏ). 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. 


    Ilwoo Cho is currently a professor at St. Ambrose University, Iowa. Dr Cho earned his PhD in Mathematics from the University of Iowa in 2005 and his master’s degree from Sungkyunkwan University in 1999. Dr Cho's research interests include free probability, operator algebra and theory, combinatorics, and groupoid dynamical systems.