On the monoid algebra associated to the monomial characters of a finite group

Given a finite group G, we study the monoid algebra R G , over a field K , generated by the monomial characters of G. In particular, we note that the integral closure of R G is contained in the algebra generated by those characters χ for which their associated Artin L-function L(s, χ) is holomorphic...

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Bibliographic Details
Published in:	Quaestiones mathematicae Vol. 46; no. 10; pp. 2065 - 2078
Main Authors:	Cimpoeaş, Mircea, Radu, Alexandru Florin
Format:	Journal Article
Language:	English
Published:	Grahamstown Taylor & Francis 03-10-2023 Taylor & Francis Ltd
Subjects:	Algebra Artin L-function Fields (mathematics) Group theory monoid algebra Monoids monomial group supercharacter theory
Online Access:	Get full text
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Summary:	Given a finite group G, we study the monoid algebra R G , over a field K , generated by the monomial characters of G. In particular, we note that the integral closure of R G is contained in the algebra generated by those characters χ for which their associated Artin L-function L(s, χ) is holomorphic at s 0 ∈ ℂ \ {1}. Also, we discuss the supercharacter theoretic case.
ISSN:	1607-3606 1727-933X
DOI:	10.2989/16073606.2022.2142862