Classical Clifford Algebras

Operator-Algebraic and Free-Probabilistic Approaches

Ilwoo Cho (Saint Ambrose University, Iowa)

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English

Chapman & Hall/CRC
08 April 2024

Algebra; Number theory; Calculus & mathematical analysis; Probability & statistics

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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.

Features

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

By: Ilwoo Cho (Saint Ambrose University Iowa)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 408g
ISBN: 9781032637112
ISBN 10: 1032637110
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 126
Publication Date: 08 April 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

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 (MG Ø A; T Ø ⴏ). 12. Deformed Semicircular Laws on (MG Ø 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.