“Quantum Groups”
E884938
foundational work in mathematical physics
foundational work in representation theory
mathematics book
monograph
“Quantum Groups” is a foundational work in mathematical physics and representation theory that introduced the concept of quantum groups, deforming classical Lie groups and algebras and profoundly influencing modern algebra and quantum integrable systems.
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| Quantum Groups | 0 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
foundational work in mathematical physics
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foundational work in representation theory ⓘ mathematics book ⓘ monograph ⓘ |
| coreConcept |
Hopf algebra structure
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antipode ⓘ braid group representations ⓘ comultiplication ⓘ counit ⓘ deformation parameter q ⓘ q-analogues of classical objects ⓘ quantum enveloping algebra U_q(g) ⓘ quasitriangular Hopf algebras ⓘ |
| describes |
deformations of classical Lie algebras
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deformations of classical Lie groups ⓘ symmetries in quantum integrable models ⓘ |
| field |
algebra
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mathematical physics ⓘ quantum integrable systems ⓘ representation theory ⓘ |
| hasNotion |
braided tensor categories
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q-characters of representations ⓘ quantum deformation of universal enveloping algebras ⓘ quantum dimensions ⓘ |
| influenceOn |
category theory approaches to quantum algebra
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knot invariants ⓘ low-dimensional topology ⓘ modern algebra ⓘ noncommutative geometry ⓘ representation theory of Lie algebras ⓘ representation theory of Lie groups ⓘ theory of quantum integrable systems ⓘ |
| mathematicalArea |
Lie theory
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noncommutative algebra ⓘ quantum algebra ⓘ topological quantum field theory ⓘ |
| topic |
Hopf algebras
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R-matrices ⓘ Yang–Baxter equation NERFINISHED ⓘ deformation of Lie algebras ⓘ deformation of Lie groups ⓘ q-deformations ⓘ quantum groups ⓘ quantum universal enveloping algebras ⓘ |
| usedIn |
construction of quantum invariants of knots and links
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exactly solvable models in statistical mechanics ⓘ quantum inverse scattering method ⓘ solutions of the Yang–Baxter equation ⓘ |
Referenced by (1)
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