Open Presentation by L.M. Ionescu,
Rota-Baxter Algebras IV: Splitting an RBA
1. "Derived Products"
- Definition: L/R -actions of A on A+/-
- Interpretation: "vector fields" on a bundle
- RBAs, graded case: RBA <=> Im(R) subalgebra <=> A=A+ ⊕
A-. proof. ...
2. The χ map ("straightening"
- Theorem ∀(A,R) complete filtered RBA ∃!
χ:A1->A1 "complementing" the BCH-deformation.
3. Comparing + and ⊕ (the
- BCH-formula is a deformation via transfer of structure, of
the abelian "product" on g=A1
- The deformed convolution ∗
- Corollary (New): chi=(R+*R-)-1
- Interpretation: 1) tranzition function, 2) R-'s failure of being the
convolution inverse of R+
(to be continued)
- Conjecture about RB-groups (factorizable groups): (A,R) complete RBA
=> (G=1+g, Cexp(Rχ)) is an RB-group pf. ...