06-1350/Class Notes for Thursday November 16
Formulas are a Chore (Bore?)
- Sweeping clean a tree and .
- is a VS-algebra (see more at VS, TS and TG Algebras).
- In the coordinates above, write the TRΦB relations in various algebraic notations.
- R4: or (B1aB2aΦ1a;B1bB2b;B1cB2aΦ1b;B2cΦ1c) = (Φ2aB3a;Φ2aB3b;Φ2bB3c;Φ2cB3c).
- R3: or (B1aB2aB3a;B1bB2b;B1cB2aB3b;B2cB3c) = (B4aB5aB6a;B4aB5bB6b;B4bB6c;B4cB5cB6a).
- R2: or .
- R1: .
- But for now, skip the writing of the following relations:
- Symmetry of Φ and of .
- u, d and
- Idempotence for T, R, Φ and .
- in terms of Φ and R and R in terms of T.
Exponentiation is a Miracle
- Description of the problem.
- Beads and strands.
- The perturbative approach, linearization.
- The syzygies: relations between the errors.
- The Hochschild complex and homology.