Representation theory of diffeomorphism groups information
Representation theory of the symmetries of manifolds
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In mathematics, a source for the representation theory of the group of diffeomorphisms of a smooth manifold M is the initial observation that (for M connected) that group acts transitively on M.
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for the representationtheoryof the groupofdiffeomorphismsof a smooth manifold M is the initial observation that (for M connected) that group acts transitively...
specifically in the representationtheoryofgroups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...
diffeomorphism; those equivalent to a diffeomorphism leaving a simple closed curve invariant; and those equivalent to pseudo-Anosov diffeomorphisms....
the more general theoryofrepresentationtheoryof semisimple groups, largely due to Élie Cartan and Hermann Weyl, but the Lorentz group has also received...
formulation Representationtheoryof the Poincaré group Wigner's classification Pauli–Lubanski pseudovector Representationtheoryof the diffeomorphismgroup Rotation...
For such groups, a typical goal ofrepresentationtheory is to classify all finite-dimensional irreducible representations of the given group, up to isomorphism...
all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods ofgrouptheory have influenced...
important to diverse areas of mathematics such as Galois theory, invariant theory, the representationtheoryof Lie groups, and combinatorics. Cayley's...
invariance and diffeomorphism invariance reflect a redundancy in the description of the system. An alternative theoryof gravitation, gauge theory gravity,...
adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie...
of solutions to Gauss's law and spatial diffeomorphism constraints that led Rovelli and Smolin to consider the loop representation in gauge theories and...
derivation of this fact) is the symmetry algebra of two-dimensional conformal field theory. Diffeomorphismgroupsof compact manifolds of larger dimension...
representationtheory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and...
even dimension Dr, where n = 2r. Since the group SO(n) is not simply connected, the representationtheoryof the orthogonal Lie algebras includes both...
aspects of the theoryof finite groups in great depth, especially the local theoryof finite groups and the theoryof solvable and nilpotent groups. As a...
the representationtheoryof more general finite groups. In the complex case, a representationof a cyclic group decomposes into a direct sum of linear...
of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theoryof abelian groups...
algebraic groups are classified by Dynkin diagrams, as in the theoryof compact Lie groups or complex semisimple Lie algebras. Reductive groups over an...
particularly tractable representationtheory because of the Peter–Weyl theorem. Just like simple complex Lie algebras, centerless compact Lie groups are classified...
specifically in grouptheory, the phrase groupof Lie type usually refers to finite groups that are closely related to the groupof rational points of a reductive...
quantum field theory, it is very common to call SL(2, C) the Lorentz group, with the understanding that SO+(1, 3) is a specific representation (the vector...
reason for the importance of reductive groups comes from representationtheory. Every irreducible representationof a unipotent group is trivial. More generally...
all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods ofgrouptheory have influenced...
mathematics, the classification of finite simple groups is a result ofgrouptheory stating that every finite simple group is either cyclic, or alternating...
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