Invariant Fields of Symplectic and Orthogonal Groups

Details Invariant Fields of Symplectic and Orthogonal Groups Invariant Fields of Symplectic and Orthogonal Groups

2001-02-28

arxiv.org/abs/math/0102226v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

The projective orthogonal and symplectic groups $PO_n(F)$ and $PSp_n(F)$ have a natural action on the $F$ vector space $V' = M_n(F) \oplus ... \oplus M_n(F)$. Here we assume $F$ is an infinite field of characteristic not 2. If we assume there is more than one summand in $V'$, then the invariant fields $F(V')^{PO_n}$ and $F(V')^{PSp_n}$ are natural objects. They are, for example, the centers of generic algebras with the appropriate kind of involution. This paper considers the rationality properties of these fields, in the case $1,2$ or 4 are the highest powers of 2 that divide $n$. We derive rationality when $n$ is odd, or when 2 is the highest power, and stable rationality when 4 is the highest power. In a companion paper [ST] joint with Tignol, we prove retract rationality when 8 is the highest power of 2 dividing $n$. Back in this paper, along the way, we consider two generic ways of forcing a Brauer class to be in the image of restriction.

Affiliated with

Also associated with

No associations

Rating

Invariant Fields of Symplectic and Orthogonal Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariant Fields of Symplectic and Orthogonal Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant Fields of Symplectic and Orthogonal Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-298920