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 “≼-morphisms” preserving a surpassing relation≼that replaces equality. We provide versions of the PBW (Poincaré-BirkhoffWitt) Theorem in these categories.
| Original language | English |
|---|---|
| Pages (from-to) | 71-110 |
| Number of pages | 40 |
| Journal | Communications in Mathematics |
| Volume | 32 |
| Issue number | 2 Special issue |
| DOIs | |
| State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 Letterio Gatto and Louis Rowen.
Funding
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.
| Funders | Funder number |
|---|---|
| INDAM-GNSAGA | RIB23GATLET |
| Israel Science Foundation | 1994/20 |
Keywords
- Filiform
- Krasner
- Lie
- PBW
- bracket
- cross product
- involution
- pairs
- pre-negation map
- semialgebra
- surpassing relation