Burnside-Brauer Theorem and Character Products in Table Algebras
نویسنده
چکیده
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-Brauer Theorem on finite groups for table algebras.
منابع مشابه
Burnside-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 کاملMartingales and Character Ratios
Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burn...
متن کاملNoncrossed Products in Witt’s Theorem
Since Amitsur’s discovery of noncrossed product division algebras more than 35 years ago, their existence over more familiar fields has been an object of investigation. Brussel’s work was a culmination of this effort, exhibiting noncrossed products over the rational function field k(t) and the Laurent series field k((t)) over any global field k — the smallest possible centers of noncrossed prod...
متن کاملCharacters of Brauer's Centralizer Algebras
Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...
متن کاملOn the Semi-simplicity of the Cyclotomic Brauer Algebras
In this paper, a criterion on the semi-simplicity of the cyclotomic Brauer algebras is given. This result can be considered as a generalization of Wenzl’s theorem on Brauer algebras [27], which was known as Hanlon-Wales conjecture before.
متن کامل