Lie product formula [SEP] named after
Lie product formula
In mathematics, the Lie product formula, named for Sophus Lie (1875), states that for arbitrary "n" × "n" real or complex matrices "A" and "B",
where "e" denotes the matrix exponential of "A". The Lie–Trotter product formula and the Trotter–Kato theorem extend this to certain unbounded linear operators "A" and "B".
This formula is an analogue of the classical exponential law
which holds for all
Cartan formula
In mathematics, Cartan formula can mean:
- one in differential geometry: formula_1, where formula_2, and formula_3 are Lie derivative, exterior derivative, and interior product, respectively, acting on differential forms. See interior product for the detail. It is also called the Cartan homotopy formula or Cartan magic formula. This formula is named after Élie Cartan.
- one in algebraic topology, which is one of the five axioms of Steenrod algebra. It reads:
See Steenrod algebra for the detail.