Titlebook: Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups; Alexander J. Hahn Textbook 1994 Springer-Verlag New York, Inc. 1994 Ari

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Matrix Theory of Clifford Algebras over Fields,ord algebra C(M) of an even dimensional quadratic space M over F is isomorphic to a matrix algebra Mat.(D) over a finite-dimensional central division algebra D over F. What subalgebra of Mat.(D) does C.(M) correspond to under such an isomorphism? If dim M is odd, then it is C.(M) that is isomorphic

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Dis(R) and Qu(R),lian group. This is the “quadratic group” Qu(R) of R. It contains the free quadratic group Qu.(R) as a subgroup and it is closely related to the group Dis(R) of Chapter 4C. The group Qu(R) will make it possible (in Chapter 13C) to extend the Arf invariant of Chapter 10D to nonsingular finitely gener

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The Arithmetic of Wq(R),ments of Br(R). as the Brauer classes of Clifford algebras of quadratic spaces over R of rank 4 and trivial Arf invariant is an important step along the way. The quadratic spaces which it provides make it possible to describe Ker . by use of the total signature. In the special case where R is the ri

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Applications of Clifford Modules, an amazing fact that Clifford algebras and Clifford modules over the real and complex numbers lie at the core of an astonishing variety of problems in differential geometry and topology. In particular, they play an important role in the analysis of vector fields on spheres, Lie groups and algebras,

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Textbook 1994tative 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 symmetr

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0172-5939 bra 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.978-0-387-94110-3978-1-4684-6311-8Series ISSN 0172-5939 Series E-ISSN 2191-6675