4 citations · 11 across the 9 of their papers we have counts for
10 papers
Groups of type over rings via TKK-algebras and their extremal elements
Seidon Alsaody, Jari Desmet
Over any commutative ring containing , we study Lie algebras of type that arise from the Tits--Kantor--Koecher (TKK) construction on a Brown algebra, a…
Groups of type and over Rings via Brown Algebras and Related Torsors
Seidon Alsaody
We study structurable algebras and their associated Freudenthal triple systems over commutative rings. The automorphism groups of these triple systems are exceptional groups of typ…
-triviality of Groups of Type Arising from the First Tits Construction
Seidon Alsaody, Vladimir Chernousov, Arturo Pianzola
Any group of type is obtained as the automorphism group of an Albert algebra. We prove that such a group is -trivial whenever the Albert algebra is obtained from the…
On the Tits-Weiss Conjecture and the Kneser-Tits Conjecture for and
Seidon Alsaody, Vladimir Chernousov, Arturo Pianzola
We prove that the structure group of any Albert algebra over an arbitrary field is -trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conje…
Albert Algebras over Rings and Related Torsors
Seidon Alsaody
We study exceptional Jordan algebras and related exceptional group schemes over commutative rings from a geometric point of view, using appropriate torsors to parametrize and expla…
On the Classification of Lie Bialgebras by Cohomological Means
Seidon Alsaody, Arturo Pianzola
We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem…
Isotopes of Octonion Algebras, G2-Torsors and Triality
Seidon Alsaody, Philippe Gille
Octonion algebras over rings are, in contrast to those over fields, not determined by their norm forms. Octonion algebras whose norm is isometric to the norm q of a given algebra C…
Lie Bialgebras, Fields of Cohomological Dimension at Most 2 and Hilbert's Seventeenth Problem
Seidon Alsaody, Alexander Stolin
We investigate Lie bialgebra structures on simple Lie algebras of non-split type . It turns out that there are several classes of such Lie bialgebra structures, and it is possib…
Composition Algebras and Outer Automorphisms of Algebraic Groups
Seidon Alsaody
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form over a field of cha…
Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
Seidon Alsaody
We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is large…