Unitary Grassmannians of Division Algebras

Unitary Grassmannians

We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided.

Algebraic space-time codes based on division algebras with a unitary involution

In this paper, we focus on the design of unitary space-time codes achieving full diversity using division algebras, and on the systematic computation of their minimum determinant. We also give examples of such codes with high minimum determinant. Division algebras allow to obtain higher rates than known constructions based on finite groups.

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Division algebras with dimension 2 t , t ∈ N

In this paper we find a field such that the algebras obtained by the Cayley-Dickson process are division algebras of dimension 2t,∀t ∈ N. Subject Classification: 17D05; 17D99. From Frobenius Theorem and from the remark given by Bott and Milnor in 1958, we know that for n ∈ {1, 2, 4} we find the real division algebras over the real field R. These are: R, C, H(the real quaternion algebra), O(the ...