Letterio Gatto ; Louis Rowen
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Lie pairs
cm:12413 -
Communications in Mathematics,
January 3, 2024,
Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
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https://doi.org/10.46298/cm.12413Lie pairsArticle
Authors: Letterio Gatto ; Louis Rowen
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Letterio Gatto;Louis Rowen
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.
Comment: 40 pages
Volume: Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
Published on: January 3, 2024
Accepted on: December 11, 2023
Submitted on: October 13, 2023
Keywords: Mathematics - Rings and Algebras, 17B99