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arXiv · 2309.03867

Lie pairs

Letterio Gatto·Louis Rowen
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Abstract

Extending the theory of systems, we introduce a theory of Lie semialgebra ``pairs'' which parallels the classical theory of Lie algebras, but with a ``null set'' replacing $0$. A selection of examples is given. These Lie pairs comprise two categories in addition to the universal algebraic definition, one with ``weak Lie morphisms'' preserving null sums, and the other with ``$\preceq$-morphisms'' preserving a surpassing relation $\preceq$ that replaces equality. We provide versions of the PBW (Poincare-Birkhoff-Witt) Theorem in these three categories.

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Letterio Gatto, Louis Rowen. 2023-09-07. Lie pairs. https://doi.org/10.46298/cm.12413

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