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Certain Examples of Deformed Preprojective Algebras and Geometry of Their *-Representations

Anton Mellit
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Abstract

We consider algebras $e_i Π^λ(Q) e_i$ obtained from deformed preprojective algebra of affine type $Π^λ(Q)$ and an idempotent $e_i$ for certain concrete value of the vector $λ$ which corresponds to the traces of $-1\in SU(2, C)$ in irreducible representations of finite subgroups of $SU(2, C)$. We give a certain realization of these algebras which allows us to construct the $C^*$-enveloping algebras for them. Some well-known results, including description of four projections with sum 2 happen to be a particular case of this picture.

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Anton Mellit. 2005-02-02. Certain Examples of Deformed Preprojective Algebras and Geometry of Their *-Representations. https://arxiv.org/abs/math/0502055

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