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This paper performed an investigation into the s-embedding of the Lie superalgebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mo stretchy="false">(</mo><mo>→</mo></mover><msup><mi>S</mi><mrow><mn>1</mn><mo>∣</mo><mn>1</mn></mrow></msup><mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>, a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>ψ</mi><mi>D</mi><mo>⊙</mo></mrow></semantics></math></inline-formula>) residing on the super-circle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>S</mi><mrow><mn>1</mn><mo>|</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>. We also introduce and rigorously define the central charge within the framework of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mo stretchy="false">(</mo><mo>→</mo></mover><msup><mi>S</mi><mrow><mn>1</mn><mo>∣</mo><mn>1</mn></mrow></msup><mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>, leveraging the canonical central extension of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>ψ</mi><mi>D</mi><mo>⊙</mo></mrow></semantics></math></inline-formula>. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mo stretchy="false">(</mo><mo>→</mo></mover><msup><mi>S</mi><mrow><mn>1</mn><mo>|</mo><mn>1</mn></mrow></msup><mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.