Path Algebras of Quivers and Representations of Locally Finite Lie Algebras
Path Algebras of Quivers and Representations of Locally Finite Lie Algebras
We explore the (noncommutative) geometry of locally simple representations of the diagonal locally finite Lie algebras |$\mathfrak{sl}(n^\infty)$|, |$\mathfrak o(n^\infty)$|, and |$\mathfrak{sp}(n^\infty)$|. Let |$\mathfrak g_\infty$| be one of these Lie algebras, and let |$I \subseteq U(\mathfrak g_\infty)$| be the non-zero annihilator of a locally simple |$\mathfrak g_\infty$|-module. We show that for …