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CATEGORIES ARISING FROM TABULAR ALGEBRAS

Published online by Cambridge University Press:  31 July 2003

R. M. GREEN
R. M. GREEN
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England e-mail: r.m.green@lancaster.ac.uk
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Abstract

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We continue the investigation of tabular algebras with trace (a certain class of associative $\mathbb{z}[v, v^{-1}]$-algebras equipped with distinguished bases) by determining the extent to which the tabular structure may be recovered from a knowledge of the structure constants. This problem is equivalent to understanding a certain category (the category of table data associated to a tabular algebra) which we introduce. The main result is that this category is equivalent to another category (the category of based posets associated to a tabular algebra) whose structure we describe explicitly.

Keywords

16B50
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 2 , May 2003 , pp. 333 - 352
Copyright
2003 Glasgow Mathematical Journal Trust