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Heisenberg group and Representation of a Lie group

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Heisenberg group and Representation of a Lie group

Heisenberg group vs. Representation of a Lie group

In mathematics, the Heisenberg group H, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form \end under the operation of matrix multiplication. In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry.

Similarities between Heisenberg group and Representation of a Lie group

Heisenberg group and Representation of a Lie group have 10 things in common (in Unionpedia): Fourier analysis, Group representation, Lie group, Mathematics, Pontryagin duality, Projective representation, Simply connected space, Stone–von Neumann theorem, Unitary representation, Vector space.

Fourier analysis

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.

Fourier analysis and Heisenberg group · Fourier analysis and Representation of a Lie group · See more »

Group representation

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

Group representation and Heisenberg group · Group representation and Representation of a Lie group · See more »

Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

Heisenberg group and Lie group · Lie group and Representation of a Lie group · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Heisenberg group and Mathematics · Mathematics and Representation of a Lie group · See more »

Pontryagin duality

In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact abelian groups, such as \R, the circle, or finite cyclic groups.

Heisenberg group and Pontryagin duality · Pontryagin duality and Representation of a Lie group · See more »

Projective representation

In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group where GL(V) is the general linear group of invertible linear transformations of V over F, and F∗ is the normal subgroup consisting of nonzero scalar multiples of the identity; scalar transformations). In more concrete terms, a projective representation is a collection of operators \rho(g),\, g\in G, where it is understood that each \rho(g) is only defined up to multiplication by a constant. These should satisfy the homomorphism property up to a constant: for some constants c(g,h). Since each \rho(g) is only defined up to a constant anyway, it does not strictly speaking make sense to ask whether the constants c(g,h) are equal to 1. Nevertheless, one can ask whether it is possible to choose a particular representative of each family \rho(g) of operators in such a way that the \rho(g)'s satisfy the homomorphism property on the nose, not just up to a constant. If such a choice is possible, we say that \rho can be "de-projectivized," or that \rho can be "lifted to an ordinary representation." This possibility is discussed further below.

Heisenberg group and Projective representation · Projective representation and Representation of a Lie group · See more »

Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

Heisenberg group and Simply connected space · Representation of a Lie group and Simply connected space · See more »

Stone–von Neumann theorem

In mathematics and in theoretical physics, the Stone–von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators.

Heisenberg group and Stone–von Neumann theorem · Representation of a Lie group and Stone–von Neumann theorem · See more »

Unitary representation

In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in case G is a locally compact (Hausdorff) topological group and the representations are strongly continuous.

Heisenberg group and Unitary representation · Representation of a Lie group and Unitary representation · See more »

Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

Heisenberg group and Vector space · Representation of a Lie group and Vector space · See more »

The list above answers the following questions

Heisenberg group and Representation of a Lie group Comparison

Heisenberg group has 96 relations, while Representation of a Lie group has 58. As they have in common 10, the Jaccard index is 6.49% = 10 / (96 + 58).

References

This article shows the relationship between Heisenberg group and Representation of a Lie group. To access each article from which the information was extracted, please visit:

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