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Multiplicatively closed Markov models must form Lie algebras


Sumner, JG, Multiplicatively closed Markov models must form Lie algebras, ANZIAM Journal, 59, (2) pp. 240-246. ISSN 1446-1811 (2017) [Refereed Article]

Copyright Statement

Copyright 2017 Australian Mathematical Society

DOI: doi:10.1017/S1446181117000359


We prove that the probability substitution matrices obtained from a continuous-time Markov chain form a multiplicatively closed set if and only if the rate matrices associated with the chain form a linear space spanning a Lie algebra. The key original contribution we make is to overcome an obstruction, due to the presence of inequalities that are unavoidable in the probabilistic application, which prevents free manipulation of terms in the Baker–Campbell–Haursdorff formula.

Item Details

Item Type:Refereed Article
Keywords:multiplicative closure, Markov models, semigroups, phylogenetics, lie algebras, continuous-time Markov chains
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Biological mathematics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Sumner, JG (Associate Professor Jeremy Sumner)
ID Code:122652
Year Published:2017
Funding Support:Australian Research Council (DP150100088)
Web of Science® Times Cited:7
Deposited By:Mathematics and Physics
Deposited On:2017-11-21
Last Modified:2022-07-04

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