Letterio Gatto ; Louis Rowen - 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") - https://doi.org/10.46298/cm.12413
Lie pairsArticle

Authors: 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.


    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

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