Open Presentation by L.M. Ionescu, 11/08/2007

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" the direct sum decomposition)

- Theorem ∀(A,R) complete filtered RBA ∃! χ:A1->A1 "complementing" the BCH-deformation.

proof. ...

3. Comparing + and ⊕ (the generic star-product)

- BCH-formula is a deformation via transfer of structure, of the abelian "product" on g=A1

- The deformed convolution ∗

- Corollary (New): chi=(R

- 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. ...

IML 11/07/2007