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Book: BottPeriodicity


See: Math, Divisions

Investigation: Relate Bott periodicity and the eight-cycle of divisions of everything.


博特周期性定理


Study and understand:

{$$\dots\rightarrow \pi_nF\rightarrow \pi_nE\rightarrow \pi_nB\rightarrow \pi_{n-1}F\rightarrow \dots$$}


Videos

Statement

Expositions

Extensions

Proofs

Related concepts

Math facts

{$\begin{pmatrix} & & \mathbb{C}_{n} & & \\ & \mathbb{H}_{n} & & \mathbb{R}_{n} & \\ \mathbb{H}_{n} \times \mathbb{H}_{n} & & & & \mathbb{R}_{n} \times \mathbb{R}_{n} \\ & \mathbb{H}_{n} & & \mathbb{R}_{n} & \\ & & \mathbb{C}_{n} & & \end{pmatrix}$}

Clifford algebra periodicity

''C_{n+8} consists of 16 x 16 matrices with entries in Cn ! For a proof you might try

Generalized Clifford Algebra has clock-shift operators.

Complex structures

Ideas

Parsiųstas iš http://www.ms.lt/sodas/Book/BottPeriodicity
Puslapis paskutinį kartą pakeistas 2019 birželio 17 d., 16:13