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Yangian of the periplectic Lie superalgebra

Maxim Nazarov

Abstract

We study in detail the Yangian of the periplectic Lie superalgebra. For this Yangian we verify an analogue of the Poincaré-Birkhoff-Witt Theorem. Moreover we introduce a family of free generators of the centre of this Yangian.

Yangian of the periplectic Lie superalgebra

Abstract

We study in detail the Yangian of the periplectic Lie superalgebra. For this Yangian we verify an analogue of the Poincaré-Birkhoff-Witt Theorem. Moreover we introduce a family of free generators of the centre of this Yangian.
Paper Structure (27 sections, 28 theorems, 210 equations)

This paper contains 27 sections, 28 theorems, 210 equations.

Table of Contents

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. ...and 12 more sections

Key Result

theorem 1

The rational function $R{ }(u\,,{ } v)$ satisfies the Yang-Baxter equation in the algebra $(\operatorname{End} {\mathbb{C}}^{{ } N|N})^{\otimes{ } 3}({ } u,v,w{ })$

Theorems & Definitions (48)

  • theorem 1
  • proof
  • proposition 1
  • proof
  • proposition 2
  • proof
  • proposition 3
  • proof
  • proposition 4
  • proof
  • ...and 38 more