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The two-dimensional "spin 1/2" representation of the Lie algebra so(3), for example, does not correspond to an ordinary (single-valued) representation of the group SO(3). (This fact is the origin of statements to the effect that "if you rotate the wave function of an electron by 360 degrees, you get the negative of the original wave function.")
Representation theory depends upon the type of algebraic object being represented. There are several different classes of groups, associative algebras and Lie algebras, and their representation theories all have an individual flavour. Representation theory depends upon the nature of the vector space on which the algebraic object is represented.
This is a list of representation theory topics, by Wikipedia page. See also list of harmonic analysis topics , which is more directed towards the mathematical analysis aspects of representation theory.
This is a list of mathematical theories. Almgren–Pitts min-max theory; ... Ramsey theory; Random matrix theory; Representation theory; Ring theory; Scheme theory ...
Representation theory studies properties of abstract groups via their representations as linear transformations of vector spaces. Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets .
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...
AP Physics C: Mechanics and AP Physics 1 are both introductory college-level courses in mechanics, with the former recognized by more universities. [8] The AP Physics C: Mechanics exam includes a combination of conceptual questions, algebra-based questions, and calculus-based questions, while the AP Physics 1 exam includes only conceptual and algebra-based questions.
Visual representation of a Schwarzschild wormhole. Wormholes have never been observed, but they are predicted to exist through mathematical models and scientific theory. Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena.