PreprintCC BY 4.0arXiv
On the number of modular pairs in finite dimensional Lie algebras on finite fields
Abstract
Given a finite dimensional Lie algebra L on a finite field 𝔽pn of prime power order pn (with n positive integer and p prime), we consider the number of modular pairs (A,B) in the lattice of all subalgebras ℒ(L) and introduce the notion of ``subalgebra commutativity degree'' of L. This represents the probability to find that two randomly chosen subalgebras A and B of L are permutable. We investigate the subalgebra commutativity degree of L in connection with recent techniques of algebraic combinatorics and number theory, providing upper and lower bounds which may influence the structure of L. A specific study for the subalgebra commutativity degree of Heisenberg algebras is executed.
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BibTeX
@misc{muhie2026number,
title = {{On the number of modular pairs in finite dimensional Lie algebras on finite fields}},
author = {Seid Kassaw Muhie and Daniele Ettore Otera and Francesco G. Russo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19086},
eprint = {2609.19086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the number of modular pairs in finite dimensional Lie algebras on finite fields
AU - Seid Kassaw Muhie
AU - Daniele Ettore Otera
AU - Francesco G. Russo
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19086
UR - https://arxiv.org/abs/2609.19086
AB - Given a finite dimensional Lie algebra L on a finite field 𝔽_p^n of prime power order p^n (with n positive integer and p prime), we consider the number of modular pairs (A,B) in the lattice of all subalgebras ℒ(L) and introduce the notion of ``subalgebra commutativity degree'' of L. This represents the probability to find that two randomly chosen subalgebras A and B of L are permutable. We investigate the subalgebra commutativity degree of L in connection with recent techniques of algebraic combinatorics and number theory, providing upper and lower bounds which may influence the structure of L. A specific study for the subalgebra commutativity degree of Heisenberg algebras is executed.
ER -