Lie Algebras of Skew-Symmetric Elements in Simple Leavitt path algebras
Abstract
Let K be a field and E be a graph. Let LK(E) be the Leavitt path algebra of E over K with the standard involution . We investigate the set of skew-symmetric elements, KLK(E)=\x∈ LK(E) : x=-x\, and show that for any simple LK(E) containing a cycle, [KLK(E), KLK(E)]KLK(E). This provides a negative answer to a question posed by Herstein raised in 1961.
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