Ebook: Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.

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Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.

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Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-2
Notation and Terminology....Pages 3-4
Fundamental Concepts in the Theory of Algebras....Pages 5-17
Separable Algebras....Pages 18-28
Groups of Free Quadratic Algebras....Pages 29-44
Bilinear and Quadratic Forms....Pages 45-64
Clifford Algebras: The Basics....Pages 65-76
Algebras with Standard Involution....Pages 77-91
Arf Algebras and Special Elements....Pages 92-105
Consequences of the Existence of Special Elements....Pages 106-122
Structure of Clifford and Arf Algebras....Pages 123-136
The Existence of Special Elements....Pages 137-152
Matrix Theory of Clifford Algebras over Fields....Pages 153-171
Dis(R) and Qu(R)....Pages 172-193
Brauer Groups and Witt Groups....Pages 194-222
The Arithmetic of Wq(R)....Pages 223-248
Applications of Clifford Modules....Pages 249-265
Back Matter....Pages 267-287

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Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-2
Notation and Terminology....Pages 3-4
Fundamental Concepts in the Theory of Algebras....Pages 5-17
Separable Algebras....Pages 18-28
Groups of Free Quadratic Algebras....Pages 29-44
Bilinear and Quadratic Forms....Pages 45-64
Clifford Algebras: The Basics....Pages 65-76
Algebras with Standard Involution....Pages 77-91
Arf Algebras and Special Elements....Pages 92-105
Consequences of the Existence of Special Elements....Pages 106-122
Structure of Clifford and Arf Algebras....Pages 123-136
The Existence of Special Elements....Pages 137-152
Matrix Theory of Clifford Algebras over Fields....Pages 153-171
Dis(R) and Qu(R)....Pages 172-193
Brauer Groups and Witt Groups....Pages 194-222
The Arithmetic of Wq(R)....Pages 223-248
Applications of Clifford Modules....Pages 249-265
Back Matter....Pages 267-287
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