These are notes on the theory of λ-rings. I started writing them as I was learning the subject myself. Later I realized that much of the content is explained (usually better) in Yau's λ-rings book and in Hazewinkel's Witt vectors notes. Nevertheless, the notes might be of some use.

The PDF can be downloaded from my website: http://www.cip.ifi.lmu.de/~grinberg/algebra/lambda.pdf

Various parts of the notes (special λ-rings, Adams operations etc.) are more or less complete. Other subjects (such as symmetric functions and Witt vectors) have not been breached. I am not actively working on these notes any longer, but I do correct mistakes as I become aware of them (let me know at [email protected] if you find one!).

• definitions of λ-rings and special λ-rings;

• examples (binomial λ-rings);

• Grothendieck's Λ(K);

• Adams operations (for special and non-special λ-rings; however the advanced facts are not being discussed);

• Todd homomorphisms;

• λ-verification principle (not in its strongest form, but in a useful enough one).

-- Darij Grinberg