projective unitary groups in a sentence

1. Pierre Deligne and George Mostow used his ideas to construct lattices in the projective unitary group.
2. This omitted certain known groups ( the projective unitary groups ), which were obtained by " twisting " the Chevalley construction.
3. O'Nan received his PhD in 1970 from Princeton University under Daniel Gorenstein with thesis " A Characterization of the Three-Dimensional Projective Unitary Group over a Finite Field ".
4. In this case the central extended group corresponding to the first projective representation of each projective unitary group is just the original unitary group of which we took the quotient by U ( 1 ) in the definition of PU.
5. The quotient of the unitary group by its center is called the "'projective unitary group "',, and the quotient of the special unitary group by its center is the "'projective special unitary group " '.
6. It's difficult to find projective unitary groups in a sentence.
7. 蒻ile Picard sought to extend the work of Schwarz in complex geometry, by means of a generalized hypergeometric function, to construct cases of equations where the monodromy was a discrete group in the projective unitary group " PU " ( 1, " n " ).
8. The above is for the classical unitary group ( over the complex numbers )  for unitary groups over finite fields, one similarly obtains special unitary and projective unitary groups, but in general \ operatorname { PSU } ( n, q ^ 2 ) \ neq \ operatorname { PU } ( n, q ^ 2 ).
9. The complex projective orthogonal group, PO ( " n ", "'C "') should not be confused with the projective unitary group, PU ( " n " ) : PO preserves a symmetric form, while PU preserves a hermitian form  PU is the symmetries of complex projective space ( preserving the Fubini Study metric ).
10. This construction is important in the study of the sporadic groups, and in much of the exceptional behavior of small classical and exceptional groups, including : construction of the Mathieu group M 24, the exceptional covers of the projective unitary group U _ 4 ( 3 ) and the projective special linear group L _ 3 ( 4 ), and the exceptional double cover of the group of Lie type G _ 2 ( 4 ).