Given a (quadratic) Jordan algebra J over a ring k, one obtains three Lie algebras, the derivation algebra, the structure algebra, and the Tits algebra. We are particularly interested in the case where J is an Albert algebra.
Tag - Albert algebra
In the first part of the lecture, I will focus on two properties of octonion algebras that are known to hold over fields but fail over arbitrary commutative rings: their enumeration by means of the Cayley-Dickson construction, and the norm equivalence theorem. In the second part, I will describe a new approach to the first Tits construction of Albert algebras that, even over fields, is more general than the classical one and sheds some new light on the classification problem for reduced Albert algebras over commutative rings.
You must be logged in to post a comment.