OAI/GroupTheory/PolycyclicRecognition/Algebra/TruncatedEnvelopingAlgebra.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

The finite truncated enveloping algebra and its faithful generators

A given nilpotent representation bounds the truncation degree and certifies injectivity. No PBW theorem or additional representation input is assumed.

  1. abbrev OAI.PolycyclicRecognition.TruncatedEnvelopingAlgebra line 24
  2. def OAI.PolycyclicRecognition.truncatedEnvelopingProjection line 28
  3. def OAI.PolycyclicRecognition.truncatedEnvelopingGenerator line 31
  4. theorem OAI.PolycyclicRecognition.truncatedEnvelopingProjection_surjective line 34
  5. theorem OAI.PolycyclicRecognition.truncatedEnvelopingProjection_eq_zero line 38
  6. theorem OAI.PolycyclicRecognition.truncatedEnvelopingGenerator_prod_eq_zero line 42
  7. theorem OAI.PolycyclicRecognition.truncatedEnveloping_adjoin_basis line 49
  8. theorem OAI.PolycyclicRecognition.truncatedEnvelopingGenerator_injective line 73
  9. theorem OAI.PolycyclicRecognition.finiteDimensional_truncatedEnvelopingAlgebra line 100