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Primitive elements in the Hall algebra of a cyclic quiver

Renda Ma

Abstract

We provide an explicit formula for primitive elements in the Hall algebras of nilpotent representations of cyclic quivers.

Primitive elements in the Hall algebra of a cyclic quiver

Abstract

We provide an explicit formula for primitive elements in the Hall algebras of nilpotent representations of cyclic quivers.
Paper Structure (34 sections, 11 theorems, 60 equations, 2 figures)

This paper contains 34 sections, 11 theorems, 60 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Ring of symmetric functions
  3. Introduction
  4. Ring of Symmetric functions
  5. Cyclic Symmetric Functions
  6. Formula of $p_n$ in ring of symmetric functions
  7. Introduction
  8. Hall algebra
  9. Introduction
  10. Finitary category
  11. Hall algebra of a finitary category
  12. Comultiplication on ${\mathbf H_{\mathcal{A}}}$
  13. ${\mathbf H_{\mathcal{A}}}$ is a bialgebra over hereditary finitary category
  14. Categories of representations of quivers
  15. Introduction
  16. ...and 19 more sections

Key Result

Lemma 3.1.1

The following formula for primitive elements in $\Lambda[t]$

Figures (2)

  • Figure :
  • Figure :

Theorems & Definitions (18)

  • Lemma 3.1.1
  • proof
  • Lemma 3.1.2
  • proof
  • Proposition 3.1.3
  • Proposition 4.3.1
  • Proposition 4.3.2
  • Definition 5.2.1
  • Definition 5.2.2
  • Example 1
  • ...and 8 more