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The algebraic and geometric classification of Jordan superalgebras

Kobiljon Abdurasulov, Roman Lubkov, Azamat Saydaliyev

Abstract

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

The algebraic and geometric classification of Jordan superalgebras

Abstract

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

Paper Structure

This paper contains 7 sections, 10 theorems, 33 equations.

Table of Contents

  1. Preliminaries
  2. Jordan superalgebras
  3. Degenerations
  4. Principal notation
  5. Methods
  6. Algebraic classification of four dimensional Jordan superalgebras
  7. Irreducible components

Key Result

Lemma 6

If $J\to J'$, then the following hold:

Theorems & Definitions (21)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Remark 5
  • Lemma 6
  • Lemma 7
  • Theorem 8
  • Theorem 9
  • Theorem 10
  • ...and 11 more