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

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

2011-11-09

arxiv.org/abs/1111.2316v1

Mathematics

Representation Theory

Scientific paper

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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