منابع مشابه
On Even Generalized Table Algebras
Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29–60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theo...
متن کاملBurnside-Brauer Theorem for Table Algebras
In the character theory of finite groups the Burnside-Brauer Theorem is a wellknown result which deals with products of characters in finite groups. In this paper, we first define the character products for table algebras and then by observing the relationship between the characters of a table algebra and the characters of its quotient, we provide a condition in which the products of characters...
متن کاملTable algebras with multiple P-polynomial structures
Using covering numbers we prove that a standard real integral table algebra (A, B) with |B| ≥ 6 has a P-polynomial structure with respect to every b = 1 in B if and only if 2|B| − 1 is prime and (A, B) is exactly isomorphic to the Bose-Mesner algebra of the association scheme of the ordinary (2|B| − 1)-gon. Then we present an example showing that this result is not true if |B| ≤ 5.
متن کاملStandard Character Condition for Table Algebras
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...
متن کاملBurnside-Brauer Theorem and Character Products in Table Algebras
In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2009
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2008.11.008