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

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

2005-02-02

arxiv.org/abs/math/0502055v1

Mathematics

Representation Theory

17 pages

Scientific paper

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.

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