scholarly journals The structure of the Brauer group and crossed products of $C_0(X)$-linear group actions on $C_0(X,\mathcal K)$

2001 ◽  
Vol 353 (9) ◽  
pp. 3685-3712 ◽  
Author(s):  
Siegfried Echterhoff ◽  
Ryszard Nest
Keyword(s):  
Linear Group ◽  
Group Actions ◽  
Brauer Group ◽  
Crossed Products

scholarly journals The invariants of orthogonal group actions

1993 ◽  
Vol 48 (2) ◽  
pp. 313-319 ◽  
Author(s):  
Li Chiang ◽  
Yu-Ching Hung
Keyword(s):  
Quadratic Form ◽  
Finite Field ◽  
Rational Function ◽  
Linear Group ◽  
Function Field ◽  
Orthogonal Group ◽  
Group Actions ◽  
Rational Function Field ◽  
Transcendental Extension

Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on , O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.

scholarly journals The Tracial Class Property for Crossed Products by Finite Group Actions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Xinbing Yang ◽  
Xiaochun Fang
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Crossed Products ◽  
Finite Group Actions ◽  
Infinite Dimensional ◽  
A Finite Group ◽  
Tracial Rokhlin Property

We define the concept of tracial𝒞-algebra ofC*-algebras, which generalize the concept of local𝒞-algebra ofC*-algebras given by H. Osaka and N. C. Phillips. Let𝒞be any class of separable unitalC*-algebras. LetAbe an infinite dimensional simple unital tracial𝒞-algebra with the (SP)-property, and letα:G→Aut(A)be an action of a finite groupGonAwhich has the tracial Rokhlin property. ThenA  ×α  Gis a simple unital tracial𝒞-algebra.

scholarly journals An Equivariant Theory for the Bivariant Cuntz Semigroup

2018 ◽  
Vol 61 (2) ◽  
pp. 573-598
Author(s):  
Gabriele N. Tornetta
Keyword(s):  
Compact Group ◽  
Group Actions ◽  
Crossed Products ◽  
C Algebras ◽  
Regularity Properties ◽  
Cuntz Semigroup ◽  
The One ◽  
Equivariant Extension ◽  
Equivariant Theory

AbstractWe provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored, and some well-known classification results are retrieved. Connections with crossed products are investigated, and a concrete presentation of equivariant Cuntz homology is provided. The theory that is here developed can be used to define the equivariant Cuntz semigroup. We show that the object thus obtained coincides with the one recently proposed by Gardella [‘Regularity properties and Rokhlin dimension for compact group actions’, Houston J. Math.43(3) (2017), 861–889], and we complement their work by providing an open projection picture of it.

scholarly journals The invariants of projective linear group actions

1989 ◽  
Vol 39 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Huah Chu ◽  
Ming-Chang Kang ◽  
Eng-Tjioe Tan
Keyword(s):  
Rational Function ◽  
Linear Group ◽  
Function Field ◽  
Group Actions ◽  
Direct Computation ◽  
Rational Function Field ◽  
Projective Linear Group

Let Fq be the field with q elements and let G = PGLn(Fq) or PSLn(Fq) act on Fq(x1,…,xn−1), the rational function field of n − 1 variables. Then Fq(x1,…,xn−1)G is purely transcendental over Fq. In fact, a set of n − 1 generators of Fq(x1,…xn−1)G, over Fq is exhibited. The case n = 2 is treated by direct computation.

Sign in / Sign up

Export Citation Format

Share Document