Group, Lie and Number Theory Date:  Monday, March 25, 2013 Location:  4096 East Hall (3:00 PM to 5:00 PM) Title:  Cayley property of algebraic groups Abstract:   As is well-known, any orthogonal matrix with determinant 1 and no eigenvalues equal to -1 can be obtained as the Cayley transform C(A) = (I-A)(I+A)^{-1} of a skew-symmetric matrix A. This establishes a birational isomorphism between the real orthogonal group and its Lie algebra that is equivariant with respect to the adjoint action of the group on itself and on its Lie algebra. By definition, a linear algebraic group over a field k has the Cayley property is there is exists such a equivariant birational map over k between the group and its Lie algebra. I will discuss some recent work on investigating which algebraic groups satisfy the Cayley property. Speaker:  Igor Dolgachev Institution:  UM Event Organizer:      mityab@umich.edu   Edit this event (login required). Add new event (login required). For access requests and instructions, contact math-webmaster@umich.edu Back to previous page Back to UM Math seminars/events page.