Definition & Betydelse | Engelska ordet AUTOMORPHISMS

Definition av AUTOMORPHISMS

1. böjningsform av automorphism

Exempel på hur man kan använda AUTOMORPHISMS i en mening

• These inner automorphisms form a subgroup of the automorphism group, and the quotient of the automorphism group by this subgroup is defined as the outer automorphism group.
• Some of his major contributions have been on the topics of the existence of semiregular automorphisms (see group action for an explanation of this) of vertex-transitive graphs, the existence of Hamiltonian paths and cycles in vertex-transitive graphs, and the structures of semi-symmetric graphs and half-transitive graphs.
• The rules of exponentiation imply that the composition of two such automorphisms is obtained by multiplying the exponents.
• In the case of transformation laws in quantum mechanics, the requisite automorphisms are unitary (or antiunitary) linear transformations of the Hilbert space V.
• Various constructions for these groups were first compiled in , including character tables, individual conjugacy classes and lists of maximal subgroup, as well as Schur multipliers and orders of their outer automorphisms.
• Collineations may also be viewed as the color-preserving automorphisms of the Heawood graph (see figure).
• As such, the Klein quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem.
• Möbius transformations commonly appear in the theory of continued fractions, and in analytic number theory of elliptic curves and modular forms, as they describe automorphisms of the upper half-plane under the action of the modular group.
• A result of Emil Artin allows one to construct Galois extensions as follows: If E is a given field, and G is a finite group of automorphisms of E with fixed field F, then E/F is a Galois extension.
• Counting constants, with n = 2g + 2, the collection of n points subject to the action of the automorphisms of the projective line has (2g + 2) − 3 degrees of freedom, which is less than 3g − 3, the number of moduli of a curve of genus g, unless g is 2.
• Other ways of saying this are that the group of automorphisms of the polytope acts transitively on its vertices, or that the vertices lie within a single symmetry orbit.
• Then any two Borel subgroups are conjugate by an inner automorphism, so to study outer automorphisms it suffices to consider automorphisms that fix a given Borel subgroup.
• Christopher Phillips and Nik Weaver, the existence of outer automorphisms of the Calkin algebra depends on set theoretic assumptions beyond ZFC.
• Originally, they were introduced by Alexander Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth.
• These two moduli problems parametrize the same objects, but the stacky version remembers automorphisms of vector bundles.
• This relation can be used both ways: given an outer automorphism, one can produce new representations (if the representation is not equal on conjugacy classes that are interchanged by the outer automorphism), and conversely, one can restrict possible outer automorphisms based on the character table.
• A nonabelian semisimple group cannot centralize itself, but it does act on itself as inner automorphisms.
• During the late 1960s the method of symbolic dynamics was developed to hyperbolic toral automorphisms by Roy Adler and Benjamin Weiss, and to Anosov diffeomorphisms by Yakov Sinai who used the symbolic model to construct Gibbs measures.
• the model theory of difference fields and of Frobenius automorphisms, where he proved extensions of Ax's work to this setting (including model-companions and decidability).
• Constructions of moduli spaces often proceed by first constructing a larger space parametrizing the objects in question, and then quotienting by group action to account for objects with automorphisms which have been overcounted.

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