The lower central series of the symplectic quotient of a free associative algebra

B. Bond, D. Jordan

Research output: Contribution to journalArticlepeer-review

Abstract

We study the lower central series filtration L for a symplectic quotient A=A /〈ω〉 of the free algebra A on 2n generators, where ω=∑[x , x ]. We construct an action of the Lie algebra H of Hamiltonian vector fields on the associated graded components of the filtration, and use this action to give a complete description of the reduced first component B̄1(A)=A/(L2+AL3) and the second component B =L /L , and we conjecture a description for the third component B =L /L .
Original languageEnglish
Pages (from-to)689-699
Number of pages11
JournalJournal of pure and applied algebra
Volume217
Issue number4
DOIs
Publication statusPublished - 1 Apr 2013

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