Archivio Istituzionale della RicercaExtending 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 `surpassing-morphisms'' preserving a surpassing relation that replaces equality. We provide versions of the PBW (Poincare-Birkhoff-Witt) Theorem in these three categories.
Lie pairs / Gatto, Letterio; Rowen, Louis. - In: COMMUNICATIONS IN MATHEMATICS. - ISSN 1804-1388. - ELETTRONICO. - 32:2(2024), pp. 71-110. [10.46298/cm.12413]
Lie pairs
Gatto, Letterio;
2024
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 `surpassing-morphisms'' preserving a surpassing relation that replaces equality. We provide versions of the PBW (Poincare-Birkhoff-Witt) Theorem in these three categories.
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https://hdl.handle.net/11583/2984844