Communications in Mathematical Physics

, Volume 320, Issue 3, pp 783–820 | Cite as

Representations of Super Yang-Mills Algebras

  • Estanislao HerscovichEmail author


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 an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149–158, 2002), and 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 \({{\rm {Cliff}}_{q}(k) \otimes A_{p}(k)}\), 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.


Hilbert Series Homogeneous Element Weyl Algebra Primitive Ideal Grade Vector Space 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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