Quaternionic Algebra Described by Sp(1) Representations

Author: Widdows D.

Source: Quarterly Journal of Mathematics, Volume 54, Number 4, December 2003 , pp. 463-481(19)

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Abstract:

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.

Document Type: Research article

Publication date: 2003-12-01

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.