mty::group Namespace Reference

Namespace to avoid name conflicts for groups that can have very simple names. See algebra::Type for the same reason. More...

Data Structures
class	E6
	Exceptional group of algebra \( E_6 \). See mty::algebra::E6. More...
class	E7
	Exceptional group of algebra \( E_7 \). See mty::algebra::E7. More...
class	E8
	Exceptional group of algebra \( E_8 \). See mty::algebra::E8. More...
class	F4
	Exceptional group of algebra \( F_4 \). See mty::algebra::F4. More...
class	G2
	Exceptional group of algebra \( G_2 \). See mty::algebra::G2. More...
class	Lorentz
	Lorentz group. Algebra of Lorentz: \( D_2=A_1\oplus A_1 \). More...
class	SO
	Special orthogonal group. The algebra of \( SO(N) \) is \( B_{(N-1)/2} \) if \( N \) is odd, \( D_{N/2} \) else. See mty::algebra::B and mty::algebra::D. More...
class	Sp
	Simplectic group. The algebra of \( Sp(2N) \) is \( C_N \). See mty::algebra::C. More...
class	SU
	Special unitary group. The algebra of \( SU(N) \) is \( A_{N-1} \) , see mty::algebra::A. More...
class	U1
	Abelian unitary group. mty::algebra::R is the associated SemiSimpleAlgebra. More...

Enumerations
enum	Type {   Type::Trivial,   Type::O,   Type::SO,   Type::U1,   Type::SU,   Type::Sp,   Type::E6,   Type::E7,   Type::E8,   Type::F4,   Type::G2,   Type::Lorentz }
	Enumeration of types of semi simple Lie groups. The names being very small, we use a namespace to avoid conflicts. More...

Functions
std::ostream &	operator<< (std::ostream &fout, mty::group::Type type)
	Overload of operator<< for group::Type::Type. Allows to display a string corresponding to the type of group instead of an integer. More...
ostream &	operator<< (ostream &fout, mty::group::Type type)

Detailed Description

Namespace to avoid name conflicts for groups that can have very simple names. See algebra::Type for the same reason.

Enumeration Type Documentation

Type

enum mty::group::Type

strong

Enumeration of types of semi simple Lie groups. The names being very small, we use a namespace to avoid conflicts.

Enumerator
Trivial	Trivial group {e}.
O	Orthogonal group \( O(N) \).
SO	Special orthogonal group \( SO(N) \).
U1	Commutative unitary group \( U(1) \).
SU	Special unitary group \( SU(N) \).
Sp	Symplectic group \( Sp(N) \).
E6	Group exponential of exceptionnal algebra \(E_6\).
E7	Group exponential of exceptionnal algebra \(E_7\).
E8	Group exponential of exceptionnal algebra \(E_8\).
F4	Group exponential of exceptionnal algebra \(F_4\).
G2	Group exponential of exceptionnal algebra \(G_2\).
Lorentz	Lorentz group, \( SO^+(1,3) \).

Function Documentation

operator<<()

std::ostream& mty::group::operator<<	(	std::ostream &	fout,
		mty::group::Type	type
	)

Overload of operator<< for group::Type::Type. Allows to display a string corresponding to the type of group instead of an integer.

Parameters

fout	Output flux.
obj	Type to display.

Returns

The modified flux.