Graded Identities for the Adjoont Representation of sl₂

2024/10/24 by Cássia Ferreira Sampaio, Plamen Koshlukov, Sampaio, Cássia F. +1
Computer Science · Mathematics · #16R10 #16R50 #17B01 #17B70 #Advanced Algebra and Geometry #Complexity and Algorithms in Graphs #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2411.00811

openalex publication_date 2024/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let K be a field of characteristic zero and let \mathfraksl₂ (K) be the 3-dimensional simple Lie algebra over K. In this paper we describe a finite basis for the ℤ₂-graded identities of the adjoint representation of \mathfraksl₂ (K), or equivalently, the ℤ₂-graded identities for the pair (M₃(K), \mathfraksl₂ (K)). We work with the canonical grading on \mathfraksl₂ (K) and the only nontrivial ℤ₂-grading of the associative algebra M₃(K) induced by that on \mathfraksl₂(K).

Related

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• On ℤ₂-graded polynomial identities of sl₂(F) over a finite field
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• Specht property for the graded identities of the pair (M₂(D), sl₂(D))
• ℤ-graded identities of the Lie algebras U₁