Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A view toward homomorphisms and cv-polynomials between double Ore extensions

María Camila Ramírez, Armando Reyes

Abstract

Motivated by the theory of homomorphisms and cv-polynomials of Ore extensions formulated by several mathematicians, the rol of double Ore extensions introduced by Zhang and Zhang in the classification of Artin-Schelter regular algebras of dimension four, and that there are no inclusions between the classes of all double Ore extensions of an algebra and of all length two iterated Ore extensions of the same algebra, our aim in this paper is to present a first approach toward a theory of homomorphisms and cv-polynomials between double Ore extensions. We obtain several results on the characterizations of cv-polynomials and their relations with inner derivations of the ring of coefficients of the double algebra, and show that the computation of homomorphisms corresponding to these polynomials is non-trivial. We illustrate our results with different examples including Nakayama automorphisms of trimmed double Ore extensions.

A view toward homomorphisms and cv-polynomials between double Ore extensions

Abstract

Motivated by the theory of homomorphisms and cv-polynomials of Ore extensions formulated by several mathematicians, the rol of double Ore extensions introduced by Zhang and Zhang in the classification of Artin-Schelter regular algebras of dimension four, and that there are no inclusions between the classes of all double Ore extensions of an algebra and of all length two iterated Ore extensions of the same algebra, our aim in this paper is to present a first approach toward a theory of homomorphisms and cv-polynomials between double Ore extensions. We obtain several results on the characterizations of cv-polynomials and their relations with inner derivations of the ring of coefficients of the double algebra, and show that the computation of homomorphisms corresponding to these polynomials is non-trivial. We illustrate our results with different examples including Nakayama automorphisms of trimmed double Ore extensions.
Paper Structure (6 sections, 11 theorems, 65 equations)

This paper contains 6 sections, 11 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Definitions and preliminaries
  3. Homomorphisms between double Ore extensiones
  4. Homomorphisms between trimmed double Ore extension
  5. Two-step iterated Ore extensions vs. Double Ore extensions
  6. Future work

Key Result

Proposition 2.2

Let $B = \Bbbk_P[y_1, y_2;\sigma', \delta', \tau']$. Then $B \cong \Bbbk[x_1] [x_2;\sigma_2, d_2]$ is an iterated Ore extension, where $\sigma_2$ is the algebra endomorphism of the polynomial ring $\Bbbk[x_1]$ defined by $\sigma_2(x_1) = p_{12}x_1 + \tau_2$ and $d_2$ is the $\sigma_2$-derivation of

Theorems & Definitions (33)

  • Definition 2.1: ZhangZhang2008; Carvalhoetal2011
  • Proposition 2.2: Carvalhoetal2011
  • Remark 2.3: Carvalhoetal2011
  • Proposition 2.4: Carvalhoetal2011
  • Proposition 2.5: ZhangZhang2008; Carvalhoetal2011
  • Remark 2.6: Carvalhoetal2011
  • Proposition 2.7: Carvalhoetal2011
  • Proposition 2.8: Carvalhoetal2011
  • Proposition 2.9: Carvalhoetal2011
  • Proposition 2.10: Carvalhoetal2011
  • ...and 23 more