On the undecidability of Markov properties for Lie superalgebras
Keywords:
Markov properties, Lie superalgebra, HNN-extension, Undecidability
Abstract
In this note, we address an algorithmic problem for Lie superalgebras. As a starting point, we use the Theory of Gröbner-Shirshov bases in order to find a normal form for Higman-Neumann-Neumann-extension (HNN-extension, for short) of Lie superalgebras. Then by using HNN-extension we show that there is no algorithm to determine whether a finitely presented Lie superalgebra satisfies Markov properties.