Two responses on the SO(3) question. Also, many about Simpson, Slack, Steinbrink, Smith, and Hanke. That leaves the following: > Jacob Davis jacob.d@mail.utexas.edu > Jim Krevitt krevitt@attbi.c > Pelle Salomonsson salomonsson@mathematik.su.se > Vladimir Jojic vjojic@santafe.edu > Marc Guastavino marc@texnet.qc.ca ____________________________________________________ Subject: Re: question abt SO(3) Date: Wed, 24 Jul 2002 09:54:30 -0400 (EDT) From: "Douglas C. Ravenel" > Date: Tue, 23 Jul 2002 13:54:23 -0400 (EDT) > From: Glen Takahara > > If U1,...,U5 are 5 distinct elements of SO(3), > the proper symmetric group, then I am able to > prove that U1 + ... + U5 = 0 is impossible. > However, my proof is brute force and I would > like to know if anyone has some intuition or > high-level reason why they would expect this > equality to be impossible. > If by SO(3) you mean the 3x3 orthogonal group and by addition you mean matrix addition, then the result is false. Choose a plane and consider the 5 matrices corresponding to rotations in that plane by multiples of 2\pi/5. Their sum is zero by symmetry, or by explicit calculation in the case where the plane is the XY-plane. Douglas C. Ravenel, Chair |918 Hylan Building Department of Mathematics |drav@math.rochester.edu University of Rochester |(585) 275-4413 Rochester, New York 14627 |FAX (585) 273-4655 ____________________________________________ Subject: Re: question abt SO(3) Date: Wed, 24 Jul 2002 10:20:50 -0400 (EDT) From: Walter Neumann I have never heard the terminology "proper symmetric group" (and neither mathscinet nor google have either) but assuming SO(3) means the special orthogonal group (group of orientation preserving symmetries of R^3 fixing the origin), the statement is surely wrong. It is not even true in the subgroup SO(2) (the circle group), e.g., Uj= rotation by 2j\pi/5 --walter neumann