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In this paper, we introduce an algebra $\mathcal{H}$ from a subspace latticewith respect to a fixed flag which contains its incidence algebra as a propersubalgebra. We then establish a relation between the algebra $\mathcal{H}$ andthe quantum affine algebra $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$, where $q$denotes the cardinality of the base field. It is an extension of the well-knownrelation between the incidence algebra of a subspace lattice and the quantumalgebra $U_{q^{1/2}}(\mathfrak{sl}_2)$. We show that there exists an algebrahomomorphism from $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$ to $\mathcal{H}$ andthat any irreducible module for $\mathcal{H}$ is irreducible as an$U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$-module.

An Algebra Associated with a Flag in a Subspace Lattice over a Finite Field and the Quantum Affine Algebra $U_q(\widehat{\mathfrak{sl}}_2)$