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Existence of partial transposition means representability in cylindric algebras

✍ Scribed by Miklös Ferenczi

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 112 KB
Volume: 57
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200910120

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✦ Synopsis

We show that the representability of cylindric algebras by relativized set algebras depends on the scope of the operation transposition which can be defined on the algebra. The existence of "partial transposition" assures this kind of representability of the cylindric algebra (while the existence of transposition assures polyadic representation). Further we characterize those cylindric algebras in which the operator transposition can be introduced.

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## Abstract We study the existence of solutions of the general elliptic system of partial differential equations in the space where the principal part may be represented with the help of a CLIFFORDalgebra 𝔄. We construct an integral representation and discuss the properties of the kernels.