Indecomposible division algebras of prime exponent.
Involution Matrix Algebras – Identities and Growth
2000 Mathematics Subject Classification: 16R50, 16R10.The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigations on involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras. Focusing on matrix algebras a complete description of involutions of the first kind on Mn(F)...
Involutions and trace forms on exterior powers of a central simple algebra.
Isomorphisms of generic splitting fields of simple algebras.
Isotropic subspaces for pairs of Hermitian matrices.
K-unirationality of conic bundles, the Kneser-Tits conjecture for spinor groups and central simple algebras
Multipliers of improper similitudes.
Nicely semiramified division algebras over Henselian fields.
On 14-dimensional quadratic forms in , 8-dimensional forms in , and the common value property.
On -commuting graph of matrix algebra.
On finite homomorphic images of the multiplicative group of a division algebra.
On the roots of polynomials over division algebras.
On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.
Pfaffians, central simple algebras and similtudes.
Projective homomorphisms and extensions of lattices.
Quadratic forms, division algebras and inseparable multiquadratic extensions. (Formes quadratiques, algèbres à division et extensions multiquadratiques inséparables.)
Quadratic pairs in characteristic 2 and the Witt cancellation theorem.
Representation theory of local division algebras.
Scaled trace forms of central simple algebras.
Severi-Brauer varieties of semidirect product algebras.