Lie Algebras of Skew-Symmetric Elements in Simple Leavitt path algebras

2025/03/25 by Nhi, Nguyen Huynh Thao, Khanh, Huynh Viet
#16S88 #17B20 #17B30 #17B65 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.19291

Abstract

Let K be a field and E be a graph. Let L_K(E) be the Leavitt path algebra of E over K with the standard involution ^⋆. We investigate the set of skew-symmetric elements, K_LK(E)=\x∈ L_K(E) : x^⋆=-x\, and show that for any simple L_K(E) containing a cycle, [K_LK(E), K_LK(E)]\neK_LK(E). This provides a negative answer to a question posed by Herstein raised in 1961.

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