Comparison of K-Theory Galois Module Structure Invariants

2000 ◽  
Vol 52 (1) ◽  
pp. 47-91 ◽  
Author(s):  
T. Chinburg ◽  
M. Kolster ◽  
V. P. Snaith
Keyword(s):  
Class Group ◽  
Module Structure ◽  
Galois Module ◽  
Comparison Result ◽  
Algebraic Integers ◽  
Galois Module Structure ◽  
Rings Of Algebraic Integers ◽  
K Theory

AbstractWe prove that two, apparently different, class-group valued Galoismodule structure invariants associated to the algebraic K-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations.

Hecke Algebras and Class-Group Invariants

1997 ◽  
Vol 49 (6) ◽  
pp. 1265-1280
Author(s):  
V. P. Snaith
Keyword(s):  
Finite Group ◽  
Class Group ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Module Structure ◽  
Galois Module ◽  
Algebraic Integers ◽  
Higher Dimensional ◽  
Rings Of Algebraic Integers ◽  
A Finite Group

AbstractLet G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, ψ, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]). Alternative constructions of Chinburg invariants arising fromthe Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of ψ. As an application we show that two such constructions coincide.

scholarly journals Quaternionic exercises in K-theory Galois module structure

1997 ◽  
pp. 1-29 ◽  
Author(s):  
Ted Chinburg ◽  
M Kolster ◽  
George Pappas ◽  
Victor Snaith
Keyword(s):  
Module Structure ◽  
Galois Module ◽  
Galois Module Structure ◽  
K Theory

scholarly journals Phase Transitions on C*-Algebras from Actions of Congruence Monoids on Rings of Algebraic Integers

2020 ◽  
Author(s):  
Chris Bruce
Keyword(s):  
Phase Transitions ◽  
Class Group ◽  
Number Fields ◽  
Algebraic Integers ◽  
Ring Of Integers ◽  
C Algebras ◽  
Rings Of Algebraic Integers ◽  
Beta 2 ◽  
Factor State ◽  
Type Classification

Abstract We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta \in [1,2]$, there is a unique KMS$_\beta $ state, and we prove that it is a factor state of type III$_1$. There are phase transitions at $\beta =2$ and $\beta =\infty $ involving a quotient of a ray class group. Our computation of KMS and ground states generalizes the results of Cuntz, Deninger, and Laca for the full $ax+b$-semigroup over a ring of integers, and our type classification generalizes a result of Laca and Neshveyev in the case of the rational numbers and a result of Neshveyev in the case of arbitrary number fields.

scholarly journals Scaffolds and generalized integral Galois module structure

2018 ◽  
Vol 68 (3) ◽  
pp. 965-1010 ◽  
Author(s):  
Nigel Byott ◽  
Lindsay Childs ◽  
G. Elder
Keyword(s):  
Module Structure ◽  
Galois Module ◽  
Galois Module Structure

scholarly journals Galois module structure of units in real biquadratic number fields

2004 ◽  
Vol 111 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Marcin Mazur ◽  
Stephen V. Ullom
Keyword(s):  
Number Fields ◽  
Module Structure ◽  
Galois Module ◽  
Galois Module Structure
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