OPERATOR FORMS OF THE CLASSICAL YANG–BAXTER EQUATION IN LIE SUPERALGEBRAS

Abstract

In this paper, we study the operator forms of the classical Yang–Baxter equation (CYBE) in Lie superalgebras. We introduce the notion of super [Formula: see text]-operators and give their relationship with the (standard) tensor form. There are close relationships between the CYBE in Lie superalgebras and left-symmetric superalgebras which can be interpreted through the super [Formula: see text]-operators. In particular, there are natural and explicit solutions of the CYBE in Lie superalgebras constructed from left-symmetric superalgebras.