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arXiv · 2303.17993

Short (SL2xSL2)-structures on Lie algebras

Patricia D. Beites·Alejandra S. Córdova-Martínez·Isabel Cunha·Alberto Elduque
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Abstract

S-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2xSL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J-ternary algebras of Allison, endowed with a nontrivial idempotent.

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Patricia D. Beites, Alejandra S. Córdova-Martínez, Isabel Cunha, Alberto Elduque. 2023-03-31. Short (SL2xSL2)-structures on Lie algebras. https://doi.org/10.1007/s13398-023-01541-4

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