Abstract

If [Formula: see text] is an associative algebra, then we can define the adjoint Lie algebra [Formula: see text] and Jordan algebra [Formula: see text]. It is easy to see that any associative Rota–Baxter (RB) operator on [Formula: see text] induces a Lie and Jordan RB operator on [Formula: see text] and [Formula: see text], respectively. Are there Lie (Jordan) RB operators, which are not associative RB operators? In this paper, we explore these questions for the Sweedler algebra [Formula: see text], which is a 4-dimensional non-commutative Hopf algebra. More precisely, we describe the RB operators on the adjoint Lie algebra [Formula: see text].

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