Representation spaces of the Jordan plane

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 $R=k<x,y>/(xy-yx-y^2)$. 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).

38 pages. arXiv admin note: substantial text overlap with arXiv:0903.3820, arXiv:0802.1545

References in corpus (4)

• Images of Golod-Shafarevich algebras with small growth
• Noncommutative complete intersections and matrix integrals
• Classification of secant defective manifolds near the extremal case
• Golod-Shafarevich algebras, free subalgebras and Noetherian images