Multiplicative groups of Leavitt path algebras

Bui Xuan Hai; Huynh Viet Khanh

Multiplicative groups of Leavitt path algebras

Rings and Algebras 2023-03-21 v1

Authors: Bui Xuan Hai , Huynh Viet Khanh

Abstract

In this paper, we prove that the multiplicative group of a unital non-commutative Leavitt path algebra $L_K(E)$ and Cohn path algebra $C_K(E)$ contain a non-cyclic free subgroup, provided $K$ is a non-absolute field. We also provide a description of the generators of free subgroups in term of the graph $E$ . Finally, we determine multiplicative groups of Leavitt path algebras of some special types.

Keywords

leavitt path algebras lie algebra

Cite

@article{arxiv.2303.10744,
  title  = {Multiplicative groups of Leavitt path algebras},
  author = {Bui Xuan Hai and Huynh Viet Khanh},
  journal= {arXiv preprint arXiv:2303.10744},
  year   = {2023}
}

Comments

31 pages, 11 figures

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