古典クリフォード代数：作用素環と確率アプローチ Classical Clifford Algebras : Operator-Algebraic and Free-Probabilistic Approaches (Chapman & Hall/crc Monographs and Research Notes in Mathematics)

Cho, Ilwoo

Chapman & Hall/CRC（2024/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 126 p.
• 言語 ENG
• 商品コード 9781032637112
• DDC分類 512.57

Full Description

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

Contents

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.