Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Contact Lie poset algebras of types B, C, and D

Nicholas Mayers, Nicholas Russoniello

Abstract

We extend a recently established combinatorial index formula applying to Lie poset algebras of types B, C, and D. Then, using the extended index formula, we determine a characterization of contact Lie poset algebras of types B, C, and D corresponding to posets of height one in terms of an associated graph.

Contact Lie poset algebras of types B, C, and D

Abstract

We extend a recently established combinatorial index formula applying to Lie poset algebras of types B, C, and D. Then, using the extended index formula, we determine a characterization of contact Lie poset algebras of types B, C, and D corresponding to posets of height one in terms of an associated graph.
Paper Structure (2 sections, 1 theorem, 3 equations, 3 figures)

This paper contains 2 sections, 1 theorem, 3 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries

Key Result

Theorem 10

Type-C (resp., B or D) posets $\mathcal{P}$ are in bijective correspondence with type-C (resp., B or D) Lie poset algebras $\mathfrak{p}$ as follows: and only in type-C

Figures (3)

  • Figure 1: Hasse diagram of $\mathcal{P}$
  • Figure 2: Hasse diagram of a type-C poset
  • Figure 3: (a) Hasse diagram and (b) relation graph of type-C poset

Theorems & Definitions (12)

  • Example 1
  • Definition 2
  • Example 3
  • Example 4
  • Definition 5
  • Remark 6
  • Remark 7
  • Remark 8
  • Example 9
  • Theorem 10: BCD
  • ...and 2 more