New Lie tori from Naoi tori

We define general Lie tori which generalize original Lie tori. We show that a Naoi torus is a general Lie torus. We give examples and prove several properties of general Lie tori. We also review isotopies of Lie tori, and prove that a general Lie torus is, in fact, isotopic to an original Lie torus. Finally, we suggest a very simple way of defining a Lie torus corresponding to a locally extended affine root system R, which we call a Lie R-torus.