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In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope. Classically, a point on the envelope can be thought of as the intersection of two "infinitesimally adjacent" curves, meaning the limit of intersections of ...
Conditions (1)–(3) are linear and can all be understood in terms of ordinary Lie algebras. Condition (4) is nonlinear, and is the most difficult one to verify when constructing a Lie superalgebra starting from an ordinary Lie algebra and a representation ().
In abstract harmonic analysis the notion of envelope plays a key role in the generalizations of the Pontryagin duality theory [20] to the classes of non-commutative groups: the holomorphic, the smooth and the continuous envelopes of stereotype algebras (in the examples given above) lead respectively to the constructions of the holomorphic, the ...
There are two slightly different ways to describe the N = 2 superconformal algebra, called the N = 2 Ramond algebra and the N = 2 Neveu–Schwarz algebra, which are isomorphic (see below) but differ in the choice of standard basis.
Examples of superellipses for =, =. A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows for various shapes between a rectangle and an ellipse.
A global symmetry is a symmetry applied uniformly (in some sense) to each point of a manifold. A local symmetry is a symmetry which is position dependent. Gauge symmetry is an example of a local symmetry, with the symmetry described by a Lie group (which mathematically describe continuous symmetries), which in the context of gauge theory is ...
According to [1] [2] the superconformal algebra with supersymmetries in 3+1 dimensions is given by the bosonic generators , , , , the U(1) R-symmetry, the SU(N) R-symmetry and the fermionic generators , ¯ ˙, and ¯ ˙.
Just as the Poincaré algebra generates the Poincaré group of isometries of Minkowski space, the super-Poincaré algebra, an example of a Lie super-algebra, generates what is known as a supergroup. This can be used to define superspace with N {\displaystyle {\mathcal {N}}} supercharges: these are the right cosets of the Lorentz group within ...