Sumner, Jeremy G. Multiplicatively closed Markov models must form Lie algebras. (English) Zbl 1416.17007 ANZIAM J. 59, No. 2, 240-246 (2017). Summary: 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. Cited in 8 Documents MSC: 17B45 Lie algebras of linear algebraic groups 60J27 Continuous-time Markov processes on discrete state spaces Keywords:Lie algebras; continuous-time Markov chains; semigroups; phylogenetics; probability substitution matrices; multiplicatively closed set PDFBibTeX XMLCite \textit{J. G. 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