2015/12/28 by Johanna Hennig, Hennig, J., Susan J. Sierra +1
Mathematics · #16D90 #16E50 #16G20 #16W50 #17B65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1512.08362
openalex publication_date 2015/12/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We explore the (noncommutative) geometry of locally simple representations of the diagonal locally finite Lie algebras \mathfraksl(n^∞), \mathfrak o(n^∞), and \mathfraksp(n^∞). Let \mathfrak g_∞ be one of these Lie algebras, and let I ⊆ U(\mathfrak g_∞) be the nonzero annihilator of a locally simple \mathfrak g_∞-module. We show that for each such I, there is a quiver Q so that locally simple \mathfrak g_∞-modules with annihilator I are parameterised by "points" in the "noncommutative space" corresponding to the path algebra of Q. Methods of noncommutative algebraic geometry are key to this correspondence. We classify the quivers that arise and relate them to characters of symmetric groups.