Definition, Betydelse & Synonymer | Engelska ordet AUTOMORPHISM

Definition av AUTOMORPHISM

1. (matematik) automorfi

Exempel på hur man kan använda AUTOMORPHISM i en mening

• In an algebraic structure such as a group, a ring, or vector space, an automorphism is simply a bijective homomorphism of an object into itself.
• In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent group.
• In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.
• Although symmetric groups can be defined on infinite sets, this article focuses on the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory.
• More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.
• In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the conjugating element.
• He has made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for the automorphism group of a function field.
• An invertible measure-preserving transformation on a standard probability space that obeys the 0-1 law is called a Kolmogorov automorphism.
• Note that the specific quotient set depends on a choice of maximal torus, but the resulting groups are all isomorphic (by an inner automorphism of G), since maximal tori are conjugate.
• All the subquotients of the automorphism group of a lattice in 24 dimensions called the Leech lattice:.
• For example, if f : M → M is a surjective R-endomorphism of a finitely generated module M, then f is also injective, and hence is an automorphism of M.
• A special case of this is when the group G in question is the automorphism group of the space X – here "automorphism group" can mean isometry group, diffeomorphism group, or homeomorphism group.
• In category theory, if two objects X and Y are isomorphic, then the isomorphisms between them, Iso(X,Y), form a torsor for the automorphism group of X, Aut(X), and likewise for Aut(Y); a choice of isomorphism between the objects gives rise to an isomorphism between these groups and identifies the torsor with these two groups, giving the torsor a group structure (as it has now a base point).
• It is a compact Riemann surface of genus , and is the only such surface for which the size of the conformal automorphism group attains the maximum of.
• This set of conformally equivalent Riemannian surfaces is precisely the same as all compact Riemannian surfaces of genus 3 whose conformal automorphism group is isomorphic to the unique simple group of order 168.
• The automorphism group of the complex Leech lattice is the universal cover 6 · Suz of the Suzuki group.
• In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F.
• the number of symmetries of the simple group PSL(2,8) that is the automorphism group of the Macbeath surface.
• A module homomorphism from a module M to itself is called an endomorphism and an isomorphism from M to itself an automorphism.
• While projective covers for modules do not always exist, it was speculated that for general rings, every module would have a flat cover, that is, every module M would be the epimorphic image of a flat module F such that every map from a flat module onto M factors through F, and any endomorphism of F over M is an automorphism.

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