Journal Article

Quaternionic Algebra Described by Sp(1) Representations

Dominic Widdows

in The Quarterly Journal of Mathematics

Volume 54, issue 4, pages 463-481
Published in print December 2003 | ISSN: 0033-5606
Published online December 2003 | e-ISSN: 1464-3847 | DOI:
Quaternionic Algebra Described by Sp(1) Representations

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This paper shows that representations of the unit quaternion group Sp(1) can be used to describe the most important spaces in quaternionic algebra. Sp(1) representations are found to underlie both the AH‐modules of Joyce and the sheaf‐theoretic approach to quaternionic algebra given by Quillen, giving a clearer understanding of the link between these two theories. Sp(1) representations are used to derive the algebraic structure of stable AH‐modules and their quaternionic tensor products, enabling us to obtain the algebraic structures of quaternion holomorphic functions on R4 and R3.

Journal Article.  0 words. 

Subjects: Pure Mathematics

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