On free subgroups in Leavitt path algebras

2025/03/24 by Hai Bui Xuan, Khanh Huynh Viet, Hai, Bui Xuan +1
Mathematics · #16S88 #20H20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.18558

Abstract

Let E be a graph and K a field. In this paper we prove that the multiplicative group of a unital noncommutative Leavitt path algebra L_K(E) contains non-cyclic free subgroups provided K is of characteristic 0. Further, we provide a description of the generators of such free subgroups in term of the graph E.

Citations

• A NOTE ON SUBNORMAL SUBGROUPS IN DIVISION RINGS CONTAINING SOLVABLE SUBGROUPS
• Free subgroups of division algebras

Related

• Multiplicative groups of Leavitt path algebras
• The graded structure of Leavittt path algebras viewed as partial skew group rings
• Leavitt path algebras with coefficients in a commutative ring
• K-theory for Leavitt path algebras: computation and classification
• A survey of some of the recent developments in Leavitt path algebras