Presenting degenerate Ringel–Hall algebras of cyclic quivers

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Using the generators labelled by simple and sincere semisimple modules for the Ringel–Hall algebra H q ( n ) of a cyclic quiver Δ ( n ) , we give a presentation for the degenerate algebra H 0 ( n ) . This is achieved by establishing a presentation for the generic extension monoid algebra of Δ ( n ) . As an application, we show that both the degenerate Ringel–Hall algebra and the degenerate quantum affine s l n admit multiplicative bases.