Lie pairs

Letterio Gatto, Louis Rowen

Research output: Contribution to journalArticlepeer-review


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 “≼-morphisms” preserving a surpassing relation≼that replaces equality. We provide versions of the PBW (Poincaré-BirkhoffWitt) Theorem in these categories.

Original languageEnglish
Pages (from-to)71-110
Number of pages40
JournalCommunications in Mathematics
Issue number2 Special issue
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 Letterio Gatto and Louis Rowen.


The authors thank the referee for careful readings, and for sound advice on improving the presentation. The first author was supported partially by INDAM-GNSAGA, PRIN Multilinear Algebraic Geometry, and RIB23GATLET. The second author was supported by the Israel Science Foundation grant 1994/20 and the Anshel Pfeffer Chair.

FundersFunder number
Israel Science Foundation1994/20


    • Filiform
    • Krasner
    • Lie
    • PBW
    • bracket
    • cross product
    • involution
    • pairs
    • pre-negation map
    • semialgebra
    • surpassing relation


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