Ustun Yildirim's homepage

Associative and Cayley Grassmannians (GSTGC 2018)

Lecture notes on $G_2$ - GGTI 2019 Summer Workshop

Introduction to G2 Geometry - GGTI Summer Workshop 2019

Github

Octonions and Cayley Grassmannian repository

I have written some code in Haskell to help me with my calculations. They are intended to be used in an Haskell interpreter but you may always fork the repository to suit your own needs or email me if you want to contribute. Specifically, it is helpful with

• complex octonions (of course, you can restrict to any subalgebra or if you only use real coefficients, you get the octonions with the positive definite metric)
• Laurent polynomials
• Jacobian calculations
• matrices (including induced matrices on exterior algebra)
• multiple cross products
• associative, coassociative and Cayley calibrations
• a little bit of exterior algebra calculus
• and more