Lie bialgebra structures on 2-step nilpotent graph algebras

2016/07/01 by Farinati, Marco A., Jancsa, A. Patricia
#17B62 (Primary) #81R50 17B40 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1607.00300

Abstract

We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebras coming from graphs, we describe these extra properties in a very easy graph-combinatorial way. We exhibit applications for \mathfrak f_n, the free 2-step nilpotent Lie algebra.

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