Abstract
We study the Zariski cancellation problem for Poisson algebras in three variables. In particular, we prove those with Poisson bracket either being quadratic or derived from a Lie algebra are cancellative. We also use various Poisson algebra invariants, including the Poisson Makar–Limanov invariant, the divisor Poisson subalgebra, and the Poisson stratiform length, to study the skew cancellation problem for Poisson algebras.
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Gaddis, J., Wang, X. & Yee, D. Cancellation and skew cancellation for Poisson algebras. Math. Z. 301, 3503–3523 (2022). https://doi.org/10.1007/s00209-022-03026-3
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DOI: https://doi.org/10.1007/s00209-022-03026-3
Keywords
- Zariski cancellation problem
- Poisson algebra
- Locally nilpotent derivation
- Divisor subalgebra
- Stratiform algebra