special unitary group उदाहरण वाक्य

उदाहरण वाक्य

1. The above exceptional isomorphisms involving the projective special linear groups are almost all of the exceptional isomorphisms between families of finite simple groups; the only other exceptional isomorphism is PSU ( 4, 2 ) C " PSp ( 4, 3 ), between a projective special unitary group and a projective symplectic group.
2. Young diagrams also parametrize the irreducible polynomial representations of the general linear group ( when they have at most nonempty rows ), or the irreducible representations of the special linear group ( when they have at most nonempty rows ), or the irreducible complex representations of the special unitary group ( again when they have at most nonempty rows ).
3. For instance, the special orthogonal group SO ( 3 ) and the special unitary group SU ( 2 ) give rise to the same Lie algebra, which is isomorphic to "'R "'3 with the cross-product, while SU ( 2 ) is a simply-connected twofold cover of SO ( 3 ).
4. For example, P?U is used for the semilinear analogs of the projective special unitary group PSU . Note however, that it is only recently noticed that these generalized semilinear groups are not well-defined, as pointed out in  isomorphic classical groups " G " and " H " ( subgroups of SL ) may have non-isomorphic semilinear extensions.
5. There is a division algebra " D " with center " l " and degree over " l " 3 or 1, with an involution of the second kind which restricts to the nontrivial automorphism of " l " over " k ", and a nontrivial Hermitian form on a module over " D " of dimension 1 or 3 such that " G " is the special unitary group of this Hermitian form . ( As a consequence of and the work of Cartwright and Steger, " D " has degree 3 over " l " and the module has dimension 1 over " D " . ) There is one real place of " k " such that the points of " G " form a copy of PU ( 2, 1 ), and over all other real places of " k " they form the compact group PU ( 3 ).