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Jordan type of full Perazzo algebras

Pedro Macias Marques, Rosa M. Miró-Roig, Josep Pérez

Abstract

In this paper, we compute all possible Jordan types of linear forms $\ell$ in any full Perazzo algebra $A$. In some cases we are also able to compute the corresponding Jordan degree type, which is a finer invariant.

Jordan type of full Perazzo algebras

Abstract

In this paper, we compute all possible Jordan types of linear forms in any full Perazzo algebra . In some cases we are also able to compute the corresponding Jordan degree type, which is a finer invariant.

Paper Structure

This paper contains 7 sections, 4 theorems, 46 equations.

Table of Contents

  1. introduction
  2. Background material
  3. Hilbert functions of Artinian Gorenstein algebras
  4. Artinian Gorenstein algebras and Macaulay--Matlis duality
  5. Jordan type of a graded Artinian algebra
  6. Perazzo algebras
  7. Jordan type of a full Perazzo algebra

Key Result

Theorem 3.2

Let $A_F=R/\mathop{\mathrm{Ann}}\nolimits_RF$ be a full Perazzo algebra, with and consider any linear form Then the Jordan type of $\ell$ in $A_F$ is one of the following Furthermore, in cases jordanTypeMax and jordanTypeMiddle the corresponding Jordan degree--types are respectively.

Theorems & Definitions (19)

  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Definition 2.4
  • Example 2.5
  • Definition 2.6
  • Definition 2.8
  • Definition 2.9
  • Example 3.1
  • Theorem 3.2
  • ...and 9 more