2011/03/31 by Estanislao Herscovich · 6 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Clifford algebra #Gauge (firearms) #Gauge theory #Lie algebra #Lie conformal algebra #Mathematical physics #Mathematics #Nest algebra #Nilpotent #Non-associative algebra #Noncommutative and Quantum Gravity Theories #Pure mathematics #Quotient #Representation theory #Yang–Mills existence and mass gap #math-ph #math.MP #math.RT #msc:13N10 #msc:16S32 #msc:17B35 #msc:17B56 #msc:70S15 #msc:81T13
paper · pdf · doi:10.1007/s00220-012-1648-z
published in Communications in Mathematical Physics 320(3), 783-820 (Springer Science+Business Media)
arxiv created 2011/05/17 · openalex publication_date 2012/12/15 · arxiv updated 2015/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are a generalization of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in \citeCD02, but in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras \Cliffq(k) ⊗ Ap(k), for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.