Crossing cubic Lie algebras

Abstract

<p>An interval-valued fuzziness structure is an effective approach addressing ambiguity and for expressing people's hesitation in everyday situations. An $ \mathcal{N} $-structure is a novel technique for solving practical problems. This is beneficial for resolving a variety of issues, and a lot of progress is being made right now. In order to develop crossing cubic structures ($ \mathcal{CCS}s $), Jun et al. amalgamate interval-valued fuzziness and $ \mathcal{N} $-structures. In this manuscript, our main contribution is to originate the concepts of crossing cubic ($ \mathcal{CC} $) Lie algebra, $ \mathcal{CC} $ Lie sub-algebra, ideal, and homomorphism. We investigate some properties of these concepts. In a Lie algebra, the construction of a quotient Lie algebra via the $ \mathcal{CC} $ Lie ideal is provided. Furthermore, the $ \mathcal{CC} $ isomorphism theorems are presented.</p>