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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=kx, y/(xy-yx-y(2)). A complete description of irreducible components of the representation variety mod(R, n) is obtained for any dimension n, it is shown that the representation variety is equidimensional. We investigate the influence of the property of the noncommutative Koszul (or Golod-Shafarevich) complex to be a DG-algebra resolution of an algebra, on the structure of representation spaces. It is shown that the Jordan plane provides a new example of representational complete intersection (RCI), which is not a preprojective algebra.

Original language | English |
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Pages (from-to) | 3507-3540 |

Number of pages | 34 |

Journal | Communications in Algebra |

Volume | 42 |

Issue number | 8 |

DOIs | |

Publication status | Published - 3 Aug 2014 |

## Keywords

- Golod-Shafarevich complex
- Irreducible components
- (noncommutative complete intersections) NCCI
- Representation spaces
- (representational complete intersections) RCI
- Primary 16G30
- 16G60
- 16D25
- Secondary 16A24
- HILBERT SERIES
- WEYL ALGEBRA
- AUTOMORPHISMS
- VARIETIES
- MATRICES

## Projects

- 1 Finished