Primitive elements in Ringel-Hall algebras of tame hereditary algebras
Abstract
We study primitive elements in the Ringel-Hall algebra H(A) of an algebra A over a finite field associated with a quiver with automorphism. When A is a tame hereditary algebra, we give a description of primitive elements in H(A) which generalizes and improves a result of Hennecart (IMRN 2021) for tame quivers. Moreover, we obtain an identity concerning primitive elements in the subalgebra of H(A) generated by regular A-modules which enables us to construct an explicit basis for the space of primitive elements in H(A).
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