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Quantum cluster algebras. (English) Zbl 1124.20028
The authors introduce and study quantum deformations of cluster algebras. The latter form a family of commutative rings which can be used in the theory of semisimple groups. To deform such algebras can be useful in Teichmüller theory. After recalling the relevant facts about cluster algebras, the authors construct and study the quantum cluster algebras. Examples in relation with Bruhat cells are also given.

20G05 Representation theory for linear algebraic groups
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16G20 Representations of quivers and partially ordered sets
16S80 Deformations of associative rings
20G42 Quantum groups (quantized function algebras) and their representations
14M17 Homogeneous spaces and generalizations
22E46 Semisimple Lie groups and their representations
Full Text: DOI arXiv
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