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arXiv · 1111.2316

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

Ben Bond·David Jordan
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Abstract

We study the lower central series filtration L_k for a symplectic quotient A=A_{2n}/ of the free algebra A_{2n} on 2n generators, where w=\sum [x_i,x_{i+n}]. We construct an action of the Lie algebra H_{2n} 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 \bar{B}_1(A)= A/(L_2 + AL_3) and the second component B_2=L_2/L_3, and we conjecture a description for the third component B_3=L_3/L_4.

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Ben Bond, David Jordan. 2011-11-09. The lower central series of the symplectic quotient of a free associative algebra. https://doi.org/10.1016/j.jpaa.2012.08.006

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