Irreducible modules over finite simple Lie pseudoalgebras IV.\n Non-primitive pseudoalgebras

2020/05/15 by Alessandro D’Andrea, D'Andrea, Alessandro · 3 citations
Mathematics · Physics and Astronomy · #17B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2005.07470

openalex publication_date 2020/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let d \⊂ d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the\ncorresponding universal enveloping algebras endowed with the cocommutative Hopf\nalgebra structure. We show that if L is a primitive Lie pseudoalgebra over H\nthen all finite irreducible L' = Cur_H^H' L-modules are of the form\nCur_H^H' V, where V is an irreducible L-module, with a single class of\nexceptions. Indeed, when L = H(d, \χ, \ω), we introduce non current\nL'-modules that are obtained by modifying the current pseudoaction with an\nextra term depending on an element t \∈ d' \∖ d, which must satisfy\nsome technical conditions. This, along with results from [BDK1, BDK2, BDK3],\ncompletes the classification of finite irreducible modules of finite simple Lie\npseudoalgebras over the universal enveloping algebra of a finite-dimensional\nLie algebra.\n

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