Standard Character Condition for Table Algebras
| Autor: | Amir Rahnamai Barghi, Javad Bagherian |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Applied Mathematics
Adjacency algebra Theoretical Computer Science Dual (category theory) Combinatorics Character (mathematics) Association scheme Computational Theory and Mathematics If and only if Discrete Mathematics and Combinatorics Table (database) Geometry and Topology Algebra over a field Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 17 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/385 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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