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arXiv · 1209.0746

Representation spaces of the Jordan plane

Natalia K. Iyudu
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Abstract

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane $R=k / (xy-yx-y^2)$. 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).

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Natalia K. Iyudu. 2012-09-04. Representation spaces of the Jordan plane. https://arxiv.org/abs/1209.0746

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