Categories arising from tabular algebras

Details Categories arising from tabular algebras Categories arising from tabular algebras

2002-07-11

arxiv.org/abs/math/0207097v1

Mathematics

Quantum Algebra

30 pages, AMSTeX, one inessential figure

Scientific paper

We continue the investigation of tabular algebras with trace (a certain class of associative ${\Bbb Z}[v, v^{-1}]$-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.

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