2024/06/05 by Skip Garibaldi, Garibaldi, Skip, Holger P. Petersson +3
Mathematics · #17B60 #20G10 #20G41 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 17Cxx #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 17B25
paper · pdf · doi:10.48550/arxiv.2406.02933
openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This document presents the solutions to the exercises in the book "Albert algebras over commutative rings" published by Cambridge University Press, 2024, as well as errata and addenda. The addenda include proofs, in the style of the book, showing that (A1) Albert algebras are exceptional and in particular that a central simple Jordan algebra over a field is exceptional if and only if it is an Albert algebra; (A2) A regular lattice in a real Albert algebra is also an Albert algebra; (A3) a Freudenthal algebra over a field is split by an extension of degree dividing 6; and (A4) a Freudenthal subalgebra of rank 9 in an Albert algebra can be used to describe the Albert algebra as a Tits construction.