Standard character condition for table algebras
The electronic journal of combinatorics, Tome 17 (2010)
It is well known that the complex adjacency algebra $A$ of an association scheme has a specific module, namely the standard module, that contains the regular module of $A$ as a submodule. The character afforded by the standard module is called the standard character. In this paper we first define the concept of standard character for C-algebras and we say that a C-algebra has the standard character condition if it admits the standard character. Among other results we acquire a necessary and sufficient condition for a table algebra to originate from an association scheme. Finally, we prove that given a C-algebra admits the standard character and its all degrees are integers if and only if so its dual.
DOI :
10.37236/385
Classification :
05E30, 20C15, 16P10
Mots-clés : complex adjacency algebra, association scheme, standard character, \(C\)-algebras, table algebra
Mots-clés : complex adjacency algebra, association scheme, standard character, \(C\)-algebras, table algebra
@article{10_37236_385,
author = {Amir Rahnamai Barghi and Javad Bagherian},
title = {Standard character condition for table algebras},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/385},
zbl = {1193.05166},
url = {http://geodesic.mathdoc.fr/articles/10.37236/385/}
}
Amir Rahnamai Barghi; Javad Bagherian. Standard character condition for table algebras. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/385
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