For type-A Lie poset algebras from posets of height at most two, the paper gives closed-form index formulas, classifies the Frobenius cases, and proves they are absolutely rigid.
Minimum rank of skew-symmetric matrices describ ed by a graph
1 Pith paper cite this work. Polarity classification is still indexing.
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The index of Lie poset algebras
For type-A Lie poset algebras from posets of height at most two, the paper gives closed-form index formulas, classifies the Frobenius cases, and proves they are absolutely rigid.