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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-102/1/i/solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 102 / 1 / i / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-07

For this Heisenberg Lie algebra,

[g, g] = C c, [g, C c] = 0,

because

c

belongs to the center. Thus its lower central series of a Lie algebra is

g, C c, 0

, so

g

is a two-step nilpotent Lie algebra.

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