Independence Polynomials of 2-step Nilpotent Lie Algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910210009858048 |
|---|---|
| author | Aldi, Marco Gabrielsen, Thor Grandini, Daniele Harris, Joy Kelley, Kyle |
| author_facet | Aldi, Marco Gabrielsen, Thor Grandini, Daniele Harris, Joy Kelley, Kyle |
| contents | Motivated by the Dani-Mainkar construction, we extend the notion of independence polynomial of graphs to arbitrary 2-step nilpotent Lie algebras. After establishing efficiently computable upper and lower bounds for the independence number, we discuss a metric-dependent generalization motivated by a quantum mechanical interpretation of our construction. As an application, we derive elementary bounds for the dimension of abelian subalgebras of 2-step nilpotent Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Independence Polynomials of 2-step Nilpotent Lie Algebras Aldi, Marco Gabrielsen, Thor Grandini, Daniele Harris, Joy Kelley, Kyle Rings and Algebras Combinatorics Quantum Physics Motivated by the Dani-Mainkar construction, we extend the notion of independence polynomial of graphs to arbitrary 2-step nilpotent Lie algebras. After establishing efficiently computable upper and lower bounds for the independence number, we discuss a metric-dependent generalization motivated by a quantum mechanical interpretation of our construction. As an application, we derive elementary bounds for the dimension of abelian subalgebras of 2-step nilpotent Lie algebras. |
| title | Independence Polynomials of 2-step Nilpotent Lie Algebras |
| topic | Rings and Algebras Combinatorics Quantum Physics |
| url | https://arxiv.org/abs/2504.19836 |