Symplectic representation and Symplectic vector space

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

Difference between Symplectic representation and Symplectic vector space

Symplectic representation vs. Symplectic vector space

In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ω) which preserves the symplectic form ω. Here ω is a nondegenerate skew symmetric bilinear form where F is the field of scalars. In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form.

Similarities between Symplectic representation and Symplectic vector space

Symplectic representation and Symplectic vector space have 6 things in common (in Unionpedia): Field (mathematics), Group (mathematics), Group representation, Lie algebra, Mathematics, Symplectic group.

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

Group (mathematics) and Symplectic representation · Group (mathematics) and Symplectic vector space · 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.

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Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

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Mathematics

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

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Symplectic group

In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted and, the latter is called the compact symplectic group.

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The list above answers the following questions

What Symplectic representation and Symplectic vector space have in common
What are the similarities between Symplectic representation and Symplectic vector space

Symplectic representation and Symplectic vector space Comparison

Symplectic representation has 13 relations, while Symplectic vector space has 62. As they have in common 6, the Jaccard index is 8.00% = 6 / (13 + 62).

References

This article shows the relationship between Symplectic representation and Symplectic vector space. To access each article from which the information was extracted, please visit:

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