11. As the unitary group does not contain the zero matrix, this action is free. 12. The manifold for is Cartesian product of the unitary group with a vector space of dimension. 13. The unitary group is the group of fixed points of the product of these two automorphisms. 14. Pierre Deligne and George Mostow used his ideas to construct lattices in the projective unitary group . 15. Unitary operators are paramount to quantum theory, so unitary groups are important in particle physics. 16. Thus, it can be used to determine the Clebsch Gordan series for any unitary group . 17. Such matrices form a Lie group called SU ( 2 ) ( see special unitary group ). 18. For example cocompact unitary group of a form of signature ( n, 1 ) are hyperbolic. 19. If transformation g is a member of a unitary group of transformations, then the following holds: 20. Similar equations can be written for any one-parameter unitary group of symmetries of the physical system.
