Group gradings on filiform Lie algebras
Yuri Bahturin, Michel Goze, Elisabeth Remm
TL;DR
This paper classifies abelian group gradings on nilpotent filiform Lie algebras, providing a comprehensive understanding of their structure and conditions for specific gradings.
Contribution
It offers a complete classification of gradings on filiform Lie algebras, including conditions for nontrivial cyclic gradings, advancing the structural theory of these algebras.
Findings
Classified gradings by abelian groups on filiform Lie algebras of nonzero rank
Described conditions for nontrivial cyclic gradings in rank 0 cases
Provided isomorphism classifications for these gradings
Abstract
We classify, up to isomorphism, gradings by abelian groups on nilpotent filiform Lie algebras of nonzero rank. In case of rank 0, we describe conditions to obtain non trivial -gradings.
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Taxonomy
TopicsAdvanced Topics in Algebra · Sphingolipid Metabolism and Signaling · Retinoids in leukemia and cellular processes