Characters of table algebras and applications to association schemes
نویسنده
چکیده
Hanaki [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] generalized many properties of characters of finite groups to characters of association schemes. In this paper we show that many of these properties also hold for table algebras. Our approach is not to generalize the proofs in [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] to table algebras, but to prove many stronger properties, and then obtain results in [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] as direct consequences. © 2008 Elsevier Inc. All rights reserved.
منابع مشابه
Association schemes , fusion rings , C - algebras , and reality - based algebras where all nontrivial multiplicities are equal
Multiplicities corresponding to irreducible characters are defined for reality-based algebras. These algebras with a distinguished basis include fusion rings, C-algebras, and the adjacency algebras of finite association schemes. The definition of multiplicity generalizes that for schemes. For a broad class of these structures, which includes the adjacency algebras, it is proved that if all the ...
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 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 کاملOn 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 کاملOn the character space of Banach vector-valued function algebras
Given a compact space $X$ and a commutative Banach algebra $A$, the character spaces of $A$-valued function algebras on $X$ are investigated. The class of natural $A$-valued function algebras, those whose characters can be described by means of characters of $A$ and point evaluation homomorphisms, is introduced and studied. For an admissible Banach $A$-valued function algebra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 115 شماره
صفحات -
تاریخ انتشار 2008