Admissible Mock-Lie Yang–Baxter Equations for Nijenhuis Mock-Lie Algebras

Abstract

In this paper, we introduce Nijenhuis operators on mock-Lie algebras and provide some new examples. Later, we mention that a Nijenhuis operator on a mock-Lie algebra induces a hierarchy of compatible mock-Lie algebra structures. Furthermore, we investigate the conditions under which a mock-Lie algebra is a Nijenhuis mock-Lie algebra based on the mock-Lie Yang–Baxter equation. Finally, we derive the compatible conditions between mock-Lie Yang–Baxter equation and Nijenhuis mock-Lie bialgebras.

Keywords

Mock-Lie algebra / Nijenhuis operator / Rota–Baxter operator / mock-Lie Yang–Baxter equation / mock-Lie bialgebras / 16T10 / 16T25 / 17B38

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