Topic
Ore extension
About: Ore extension is a research topic. Over the lifetime, 228 publications have been published within this topic receiving 3116 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1989TL;DR: The 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra as mentioned in this paper, and it can be used as a second-year graduate text, or as a self-contained reference.
Abstract: This 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. Material includes the basic types of quantum groups, which then serve as test cases for the theory developed.
1,098 citations
TL;DR: Cauchon et al. as discussed by the authors constructed the derivative-elimination algorithm, which consists of a sequence of changes of variables inside the division ring F=Fract(R), starting with the indeterminates (X1, X2, XN) and terminating with new variables (T1, T1, N) to generate some quantum-affine space R such that F= Fract(R ).
135 citations
TL;DR: In this article, the relation between twisted Calabi-Yau and Nakayama automorphisms of 5-dimensional Artin-Schelter regular algebras is studied.
Abstract: Suppose that $E=A[x;\sigma,\delta]$ is an Ore extension with $\sigma$ an automorphism. It is proved that if $A$ is twisted Calabi-Yau of dimension $d$, then $E$ is twisted Calabi-Yau of dimension $d+1$. The relation between their Nakayama automorphisms is also studied. As an application, the Nakayama automorphisms of a class of 5-dimensional Artin-Schelter regular algebras are given explicitly.
64 citations
TL;DR: In this paper, the finiteness conditions for infinite dimensional coalgebras, particularly right or left semiperfect co-Frobenius Hopf algebrains, are studied.
54 citations
TL;DR: In this paper, the authors consider an iterated Ore extension k[y][x;σ,δ] of the complex number field k, with δ a k-automorphism of k[x] and δ u-derivation of k [y] vanishing on k.
Abstract: Let R be an iterated Ore extension k[y][x;σ,δ] of the complex number field k, with δ a k-automorphism of k[y] and δ a u-derivation of k[y] vanishing on k. We suppose that the center of R is k. Up to a change of variables, any finite group G of k-automorphisms of R acts linearly on kx⊕D1ky. When the quotient division ring D of R is isomorphic to the Weyl skewfield D1(k)1 , then DG⋍D1 (k). In any other noncommutative case, D is isomorphic to the quantum Weyl skewfield Dq 1(k) for some q∊k∗ not a root of one, and DG⋍Ds 1(k) with s = q‖G‖.
46 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 14 |
| 2020 | 10 |
| 2019 | 7 |
| 2018 | 7 |
| 2017 | 20 |
| 2016 | 15 |