Representation spaces of the Jordan plane
  We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane $R=k<x,y>/ (xy-yx-y^2)$.   Complete description of irreducible components of the representation variety $mod (R,n)$ obtained for any dimension $n$, it is shown that the variety is equidimensional.   The influence of the property of the non-commutative Koszul (Golod-Shafarevich) complex to be a DG-algebra resolution of an algebra (NCCI), on the structure of representation spaces is studied. It is shown that the Jordan plane provides a new example of RCI (representational complete intersection). 
Natalia K. Iyudu
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