## 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

SHOWING 1-10 OF 72 REFERENCES

### 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…