mathematical structure
C3748
concept
A mathematical structure is a set (or collection of objects) equipped with specified operations, relations, or properties that satisfy given axioms, providing a framework for studying abstract patterns and relationships.
All labels observed (48)
| Label | Occurrences |
|---|---|
| mathematical theory | 56 |
| Lie group | 24 |
| algebraic structure | 21 |
| mathematical group | 16 |
| mathematical structure canonical | 15 |
| integer sequence | 13 |
| topological space | 12 |
| mathematical framework | 9 |
| finite group | 8 |
| associative algebra | 7 |
| non-abelian group | 6 |
| combinatorial structure | 4 |
| dimension theory concept | 4 |
| symmetry group | 3 |
| category-theoretic structure | 2 |
| causal structure representation | 2 |
| formal logical system | 2 |
| metric space | 2 |
| noncommutative algebra | 2 |
| number system | 2 |
| ordered field | 2 |
| stability theory | 2 |
| structure in Hodge theory | 2 |
| structure in differential geometry | 2 |
| *-algebra | 1 |
| Steiner system | 1 |
| algebraic framework | 1 |
| categorical structure | 1 |
| concept in convex analysis | 1 |
| concept in discrete mathematics | 1 |
| construction in partition theory | 1 |
| fixed-point theory | 1 |
| group theory construction | 1 |
| information geometric structure | 1 |
| mathematical field | 1 |
| mathematical notion | 1 |
| mathematical structure in general relativity | 1 |
| model-theoretic construct | 1 |
| order-theoretic concept | 1 |
| order-theoretic structure | 1 |
| second-order logical system | 1 |
| set of mathematical conditions | 1 |
| set-theoretic construct | 1 |
| set-theoretic universe | 1 |
| structure in algebraic geometry | 1 |
| structure in classical field theory | 1 |
| structure in classical mechanics | 1 |
| unique factorization domain | 1 |
Instances (220)
| Instance | Via concept surface |
|---|---|
| Kronecker delta | concept in discrete mathematics |
| Nekhoroshev theory | mathematical theory |
| Singularity Theory | mathematical theory |
| Weyl algebra | associative algebra |
| Euclidean group | mathematical group |
| E(n) | mathematical group |
| SU(2)_L | Lie group |
| Lie theory | mathematical theory |
| Schwarzschild Penrose diagram | causal structure representation |
| Peierls bracket | structure in classical field theory |
| Lie ring | algebraic structure |
| Lie pseudogroup | structure in differential geometry |
| Lie subgroup | Lie group |
| Lie group | — |
| AdS isometry group SO(2,d) | Lie group |
| Minkowski sum | concept in convex analysis |
|
von Neumann algebras
surface form:
von Neumann algebra
|
— |
| von Neumann universe | set-theoretic universe |
| OEIS A064988 | integer sequence |
| Artinian module | algebraic structure |
| Krull dimension | dimension theory concept |
| information theory | mathematical theory |
| Chern–Weil theory | mathematical theory |
| Zariski topology | structure in algebraic geometry |
| Hahn series | algebraic structure |
| Cantor set | topological space |
| Onsager algebra | — |
| Galilean group | mathematical group |
|
Dyson’s transform in number theory
surface form:
Dyson’s transform
|
construction in partition theory |
|
rotation group SO(3)
surface form:
SO(3)
|
Lie group |
| SL(2,C) | Lie group |
| SU(3) | Lie group |
| Lyapunov stability theory | stability theory |
| Jacobi bracket | structure in differential geometry |
| Frege’s system in "Grundgesetze der Arithmetik" | formal logical system |
| Menger sponge | topological space |
|
Probability Theory
surface form:
Probability theory
|
mathematical theory |
| Gröbner basis | algebraic structure |
|
Hilbert spaces
surface form:
Hilbert space
|
— |
| universal intelligence measure | mathematical framework |
| spacetime algebra | mathematical framework |
| geometric calculus | mathematical framework |
|
foundations of geometric algebra as a unified language for physics
surface form:
Foundations of geometric algebra as a unified language for physics
|
mathematical framework |
| Euclidean space | metric space |
| Herbrand interpretation | model-theoretic construct |
| de Bruijn graph | combinatorial structure |
| Weil group | mathematical group |
| Weil cohomology | mathematical theory |
| Grothendieck topology | categorical structure |
| Grothendieck category | category-theoretic structure |