REPRESENTATION SPACES OF THE JORDAN PLANE

Natalia K. Iyudu

doi:10.1080/00927872.2013.788184

REPRESENTATION SPACES OF THE JORDAN PLANE

Natalia K. Iyudu^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	3507-3540
Number of pages	34
Journal	Communications in Algebra
Volume	42
Issue number	8
DOIs	https://doi.org/10.1080/00927872.2013.788184
Publication status	Published - 3 Aug 2014

Keywords / Materials (for Non-textual outputs)

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

Access to Document

10.1080/00927872.2013.788184

Combinatorial methods in noncommutative ring theory (COIMBRA)
Smoktunowicz, A.
EU government bodies
1/06/13 → 31/05/18
Project: Research

Cite this

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title = "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=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.",

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KW - (noncommutative complete intersections) NCCI

KW - Representation spaces

KW - (representational complete intersections) RCI

KW - Primary 16G30

KW - 16G60

KW - 16D25

KW - Secondary 16A24

KW - HILBERT SERIES

KW - WEYL ALGEBRA

KW - AUTOMORPHISMS

KW - VARIETIES

KW - MATRICES

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DO - 10.1080/00927872.2013.788184

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 8

ER -

REPRESENTATION SPACES OF THE JORDAN PLANE

Abstract

Keywords / Materials (for Non-textual outputs)

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Projects

Combinatorial methods in noncommutative ring theory (COIMBRA)

Cite this