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 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: mathematical structure
Generated description
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.
Instances (220)
| Instance | Via concept surface |
|---|---|
| Poisson bracket | structure in classical mechanics |
| Sylvester sequence | integer sequence |
| renormalization group | mathematical framework |
| chaos theory | mathematical theory |
| Lie sphere group | mathematical group |
| orthogonal group O(n+1,2) | Lie group |
| Lie algebroid | — |
| Catalan numbers | integer sequence |
| Bell numbers | integer sequence |
| SO(2,d-1) | Lie group |
| Spin(2,d) | Lie group |
|
special unitary group SU(n)
surface form:
SU(n)
|
Lie group |
|
general linear group GL(n,R)
surface form:
GL(n,ℝ)
|
Lie group |
|
special linear group SL(n,R)
surface form:
SL(n,ℝ)
|
Lie group |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
Lie group |
|
special linear group SL(n,C)
surface form:
SL(n,ℂ)
|
Lie group |
| Osterwalder–Schrader axioms | set of mathematical conditions |
|
Kleene
surface form:
Kleene algebra
|
algebraic structure |
| Kleene algebra | algebraic structure |
| Hausdorff dimension | dimension theory concept |
|
Mersenne
surface form:
Mersenne number
|
integer sequence |
| OEIS A002849 | integer sequence |
| Krull–Gabriel dimension | dimension theory concept |
| Grothendieck toposes | category-theoretic structure |
| McDuff–Salamon theory of J-holomorphic curves | mathematical theory |
| Spectral Graph Theory | mathematical field |
| OEIS A002850 | integer sequence |
| OEIS A002851 | integer sequence |
| Levi-Civita field | ordered field |
|
Euclidean domains
surface form:
Euclidean domain
|
algebraic structure |
| Dedekind cut | order-theoretic structure |
| Dedekind number | integer sequence |
|
Eilenberg–MacLane spaces
surface form:
Eilenberg–MacLane space
|
topological space |
| Outer space (Culler–Vogtmann Outer space) | topological space |
| Culler–Vogtmann Outer space | topological space |
|
Abelian groups
surface form:
Abelian group
|
algebraic structure |
| Conway’s games | — |
| algebraic quantum field theory | mathematical framework |
| Lorentzian geometry | mathematical theory |
| Askey–Wilson algebra | associative algebra |
| Freidlin–Wentzell theory | mathematical theory |
| q-Onsager algebra | associative algebra |
| Fischer–Griess Monster | algebraic structure |
| McLaughlin group | finite group |
| monstrous moonshine | mathematical theory |
| PSL(2,ℤ/Nℤ) | finite group |
| SL(2,ℤ) | non-abelian group |
| PSL(2,ℝ) | Lie group |
| Mie theory | mathematical framework |
| Fibonacci sequence | integer sequence |