Quantum algebras and quivers
نویسنده
چکیده
Given a finite quiver Q without loops, we introduce a new class of quantum algebras D(Q) which are deformations of the enveloping algebra of a Lie algebra which is a central extension of sln(Π(Q)) where Π(Q) is the preprojective algebra of Q. When Q is an affine Dynkin quiver of type A, D or E, we can relate them to Γ-deformed double current algebras. We are able to construct functors between different categories of modules over D(Q). We also give some general results about ŝln(A) for a quadratic algebra A and about ĝ(C[u, v]), which we use to introduce deformed double current algebras associated to a simple Lie algebra g.
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