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Everything about Automorphism
Isomorphism of an object to itself
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: AutomorphismA 5-minute orientation
- Skim a recent paper: Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codesInfluential work since 2022
- Pick up a classic book: Automorphic Forms and Galois RepresentationsThe most-reprinted book on the subject
- Read the landmark paper: k-automorphismCited 290 times
- Go sideways: EndomorphismA closely related topic
- Go sideways: HomomorphismA closely related topic
📖 Definitions
Noun An isomorphism of a mathematical object or system of objects onto itself.
Noun The ascription to others of one's own characteristics or of one's own perceived characteristics.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
k-automorphism
Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups
On the full automorphism group of a graph
The maximal subgroups of the chevalley groups G2(q) with q odd, the Ree groups 2G2(q), and their automorphism groups
Automorphism groups and isomorphisms of Cayley digraphs
Characterization of the unit ball in ? n by its automorphism group
Spectral analysis of graphs by cyclic automorphism subgroups
Computing automorphism groups of error-correcting codes
🆕 Influential since 2022
Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes
Nonlinear automorphism of the conformal algebra in 2D and continuous $$ \sqrt{T\overline{T}} $$ deformations
A novel S-box generator using Frobenius automorphism and its applications in image encryption
Quantum computation from dynamic automorphism codes
On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and Their Consequences
📚 Books worth reading
- 📕Automorphic Forms and Galois RepresentationsMinhyong Kim, Fred Diamond · 2014
Days with LeninМаксим Горький · 1932- 📕Automorphic Forms and l-Functions for the Group GL(n,R)Dorian Goldfeld · 2006
Automorphisms of surfaces after Nielsen and ThurstonAndrew J. Casson · 1982
Vorlesungen über die theorie der automorphen functionenFricke, Robert · 1897
Modern Analysis of Automorphic Forms By ExamplePaul Garrett · 2018- 📕Analytic functions of several complex variablesCarl Ludwig Siegel · 1949
Automorphic Forms, Shimura Varieties and L-FunctionsLaurent Clozel · 1990
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Endomorphism In abstract algebra, an endomorphism is a homomorphism from a mathematical object to itself. More generally in category theory, an endomorphism is a morphism…
- Homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector…
- Symmetry in mathematics Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object…
- Inner automorphism 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…
- Isomorphism In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse…
- Group representation In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector…
- Morphism In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures…
- Adjoint representation In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations…