16 research outputs found
How to obtain division algebras used for fast-decodable space-time block codes
We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D, employing a K-automorphism tau and an invertible element d in D. These algebras appear in the construction of iterated space-time block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly look at algebras (and codes) obtained from variations of this method
Degree formula for connective K-theory
We apply the degree formula for connective -theory to study rational
contractions of algebraic varieties. Examples include rationally connected
varieties and complete intersections.Comment: 14 page
Open Problems on Central Simple Algebras
We provide a survey of past research and a list of open problems regarding
central simple algebras and the Brauer group over a field, intended both for
experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered,
compared to v
On the notion of canonical dimension for algebraic groups (in special volume in honor of Michael Artin: part I)
We define and study a numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in pn-1