English

Primitive elements in Ringel-Hall algebras of tame hereditary algebras

Representation Theory 2026-03-10 v1

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).

Keywords

Cite

@article{arxiv.2603.08169,
  title  = {Primitive elements in Ringel-Hall algebras of tame hereditary algebras},
  author = {Bangming Deng and Weihao Li},
  journal= {arXiv preprint arXiv:2603.08169},
  year   = {2026}
}