Dolan–Grady relations
E653519
algebraic relation
commutation relation
concept in mathematical physics
concept in statistical mechanics
The Dolan–Grady relations are algebraic commutation relations between two operators that generate the Onsager algebra and play a key role in the study of exactly solvable models in statistical mechanics.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic relation
ⓘ
commutation relation ⓘ concept in mathematical physics ⓘ concept in statistical mechanics ⓘ |
| appliesTo | two operators ⓘ |
| category |
exactly solvable lattice models
ⓘ
integrable structures in statistical mechanics ⓘ |
| defines | Onsager algebra generators NERFINISHED ⓘ |
| describedAs | algebraic commutation relations between two operators ⓘ |
| field |
algebra
ⓘ
mathematical physics ⓘ statistical mechanics ⓘ |
| generalizationOf | Onsager’s commutation relations ⓘ |
| hasKeyRoleIn |
construction of integrals of motion
ⓘ
integrability of lattice models ⓘ study of exactly solvable models in statistical mechanics ⓘ |
| hasMathematicalContext |
Lie algebras
NERFINISHED
ⓘ
infinite-dimensional algebras ⓘ representation theory ⓘ |
| hasOperatorType | self-adjoint operators (in many physical realizations) ⓘ |
| involves | nested commutators of two generators ⓘ |
| isPartOf | algebraic approach to integrable systems ⓘ |
| namedAfter |
Leon Dolan
NERFINISHED
ⓘ
Michael Grady NERFINISHED ⓘ |
| property | lead to closed algebra under commutation ⓘ |
| relatedTo |
Askey–Wilson algebra
NERFINISHED
ⓘ
Onsager algebra NERFINISHED ⓘ Yang–Baxter equation NERFINISHED ⓘ loop algebras ⓘ quantum integrable systems ⓘ transfer matrix methods ⓘ tridiagonal pairs ⓘ |
| role | generate the Onsager algebra ⓘ |
| satisfies | Onsager’s original algebraic structure for the Ising model ⓘ |
| usedFor |
constructing infinite sets of commuting operators
ⓘ
deriving exact spectra in integrable models ⓘ |
| usedIn |
Ising model
NERFINISHED
ⓘ
Z-invariant models ⓘ exactly solvable models ⓘ integrable models ⓘ two-dimensional lattice models ⓘ |
| yearProposed | 1982 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.