Hyperbolic cluster algebras

Details Hyperbolic cluster algebras Hyperbolic cluster algebras

2011-08-05

arxiv.org/abs/1108.1245v1

Mathematics

Representation Theory

Scientific paper

In this article, we set up for a new class of non-commutative algebras that carry a non-commutative cluster structure. This structure is related naturally to some Hyperbolic algebras like Weyl Algebras, classical and quantized universal enveloping algebras of sl2 and the quantum coordinate algebra of SL(2). The cluster structure gives rise to some combinatorial data, called cluster strings, which are used to introduce a class of representations of Weyl algebras. Irreducible and indecomposable representations are also introduced from the same data.

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