2 Citations
Albert algebras over $\mathbb {Z}$ and other rings
- MathematicsForum of Mathematics, Sigma
- 2023
Abstract Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative nonassociative algebras and also arise naturally in the context of simple affine…
ALBERT ALGEBRAS OVER Z AND OTHER RINGS
- Mathematics
- 2022
A BSTRACT . Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise naturally in the context of simple affine…
References
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Decomposability of orthogonal involutions in degree 12
- MathematicsPacific Journal of Mathematics
- 2020
A theorem of Pfister asserts that every $12$-dimensional quadratic form with trivial discriminant and trivial Clifford invariant over a field of characteristic different from $2$ decomposes as a…
The Book of Involutions
- Mathematics
- 1998
This monograph yields a comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups. It aims to provide the algebra-theoretic…
Dynkin diagrams and short Peirce gradings of Kantor pairs
- MathematicsCommunications in Algebra
- 2019
Abstract In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC2, consisting of…
On algebraic groups defined by Jordan pairs
- MathematicsNagoya Mathematical Journal
- 1979
Let G be an algebraic group over a field k, and let ψ be an action of the multiplicative group km of k on G by automorphisms. We say ψ is an elementary action if it has only the weights 0, ±1; more…
Non-abelian gradings of Lie algebras
- Mathematics
- 2017
We introduce non-abelian gradings of Lie algebras as their isotypic decompositions with respect to reductive groups of automorphisms. The main results relate to a special kind of SL3-gradings, in…
Some Groups of Transformations defined by Jordan Algebras. I.
- Mathematics
- 1959
It is well known that the Lie algebra of derivations of the exceptional Jordan algebra Ml over an algebraically closed field of characteristic 0 or over the field of reals is the exceptional Lie…