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Classification of linearly compact simple algebraic N = 6 3-algebras

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Abstract

N ≤ 8 3-algebras have recently appeared in N-supersymmetric 3-dimensional Chern–Simons gauge theories. In our previous paper we classified linearly compact simple N = 8 n-algebras for any n ≥ 3. In the present paper we classify algebraic linearly compact simple N = 6 3-algebras over an algebraically closed field \( \mathbb{F} \) of characteristic 0, using their correspondence with simple linearly compact Lie superalgebras with a consistent short \( \mathbb{Z} \)-grading, endowed with a graded conjugation. We also briey discuss N = 5 3-algebras.

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Authors and Affiliations

  1. Dipartimento di Matematica, Pura ed Applicata, Università di Padova, Padova, Italy

    Nicoletta Cantarini

  2. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Victor G. Kac

Authors
  1. Nicoletta Cantarini
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  2. Victor G. Kac
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Correspondence to Nicoletta Cantarini.

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To T.A. Springer on his 85th birthday

Partially supported by Progetto di Ateneo CPDA071244. (Nicoletta Cantarini)

Partially supported by an NSF grant and by the ERC Advanced Grant 227458 OACFT “Operator Algebras and Conformal Field Theory”. (Victor G. Kac)

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Cantarini, N., Kac, V.G. Classification of linearly compact simple algebraic N = 6 3-algebras. Transformation Groups 16, 649–671 (2011). https://doi.org/10.1007/s00031-011-9143-8

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