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Mathematics > Rings and Algebras

arXiv:2205.08838 (math)
[Submitted on 18 May 2022]

Title:Killing metrized commutative nonassociative algebras associated with Steiner triple systems

Authors:Daniel J. F. Fox
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Abstract:With each Steiner triple system there is associated a one-parameter family of commutative, nonassociative, nonunital algebras that are by construction exact, meaning that the trace of every multiplication operator vanishes, and these algebras are shown to be Killing metrized, meaning the Killing type trace-form is nondegenerate and invariant (Frobenius), and simple, except for certain parameter values. The definition of these algebras resembles that of the Matsuo algebra of the Steiner triple system, but they are different. For a Hall triple system, the associated algebra is a primitive axial algebra for a $\mathbb{Z}/2\mathbb{Z}$-graded fusion law.
Subjects: Rings and Algebras (math.RA)
Cite as: arXiv:2205.08838 [math.RA]
  (or arXiv:2205.08838v1 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.2205.08838
Journal reference: Journal of Algebra. Vol. 608, No. 15 (2022), pp. 186-213
Related DOI: https://doi.org/10.1016/j.jalgebra.2022.05.026

Submission history

From: Daniel J. F. Fox [view email]
[v1] Wed, 18 May 2022 10:10:50 UTC (30 KB)
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