THE BRAUER GROUP OF QUOTIENT SPACES BY LINEAR GROUP ACTIONS

1988 ◽  
Vol 30 (3) ◽  
pp. 455-485 ◽  
Author(s):  
F A Bogomolov
Keyword(s):  
Linear Group ◽  
Group Actions ◽  
Brauer Group ◽  
Quotient Spaces

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 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.

Cyclic p-group actions on ℝℙ3

2020 ◽  
pp. 2150192
Author(s):  
John Kalliongis ◽  
Ryo Ohashi
Keyword(s):  
Projective Space ◽  
Group Actions ◽  
Lens Space ◽  
Equivalence Classes ◽  
Real Projective Space ◽  
The Real ◽  
Quotient Spaces ◽  
Standard Action

In this paper, we classify the smooth orientation preserving cyclic [Formula: see text]-group actions on the real projective space [Formula: see text] up equivalence, where two actions are equivalent if their images are conjugate in the group of self-diffeomorphisms. We view [Formula: see text] as the lens space [Formula: see text]. We show that any such action on [Formula: see text] is conjugate to a standard action explicitly defined, and we identify the quotient spaces of these actions. In addition, we enumerate the equivalence classes.

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