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

Anton Mellit
### Abstract

We consider algebras $e_i\Pi_\lambda(Q) e_i$ obtained from deformed preprojective algebra of affine type $\Pi_\lambda(Q)$ and an idempotent $e_i$ for certain concrete value of the vector $\lambda$ 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.

Publication

*arXiv preprint* math/0502055