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Multiloop algebras determined by n commuting algebra automor-phisms of finite order are natural generalizations of the classical loop algebras that are used to realize affine Kac-Moody Lie algebras. In this paper, we obtain necessary and sufficient conditions for a Z n-graded algebra to be realized as a multiloop algebra based on a finite dimensional simple… (More)
This paper is intended to make the results of Bank research available in preliminary form to other economists to encourage discussion and suggestions for revision. The views expressed are those of the author. No responsibility for them should be attributed to the Bank of Canada.
Centreless Lie tori have been used by E. Neher to construct all extended affine Lie algebras (EALAs). In this article, we study isotopy for centreless Lie tori, and show that Neher's construction provides a 1-1 correspondence between centreless Lie tori up to isotopy and families of EALAs up to isomorphism. Also, centreless Lie tori can be coordinatized by… (More)
Synopsis This background paper answers the historical question: why did Australia adopt proportional representation for the Senate? The bare facts are well known: in 1948 the Chifley government initiated amendments to the Electoral Act to alter the existing method of counting the Senate vote which had traditionally rewarded the majority party with a… (More)
The classification of structurable tori with nontrivial involution, which was begun by Allison and Yoshii, is completed. New examples of struct-urable tori are obtained using a construction of structurable algebras from a semilinear version of cubic forms satisfying the adjoint identity. The classification uses techniques borrowed from quadratic forms over… (More)
Marine invertebrates are sources of a diverse array of bioactive metabolites with great potential for development as drugs and research tools. In many cases, microorganisms are known or suspected to be the biosynthetic source of marine invertebrate natural products. The application of molecular microbiology to the study of these relationships will… (More)
Over the last three decades there has been significant progress in the first principles methods for calculating the properties of materials at the quantum level. They have largely been based on the local density approximation (LDA) to density functional theory (DFT). However, nanoscience places new demands on these first principles methods because of the… (More)