𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Division Algebras of Degree 3 with Involution

✍ Scribed by Darrell E Haile; Max-Albert Knus

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
151 KB
Volume
184
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let D be a division algebra of degree 3 over its center K and let J be an involution of the second kind on D. Let F be the subfield of K of elements invariant under J, char F / 3. We present a simple proof of a theorem of A. Albert on the existence of a maximal subfield of D which is Galois over F with group S S 3 and prove an analog for symmetric elements of Wedderburn's Theorem on the splitting of the minimal polynomial of any element of D. These results are then applied to the theory of the Clifford algebra of a binary cubic form. ᮊ 1996 Academic Press, Inc. 2 existence of a maximal subfield of D which is Galois over F with group S S . The first step is a construction of a subspace of elements u such that

📜 SIMILAR VOLUMES

On Involutive Homogeneous Varieties and
On Involutive Homogeneous Varieties and Representations of Weyl Algebras
✍ S.C. Coutinho 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 135 KB

This paper is concerned with the geometry of minimal involutive homogeneous varieties in complex affine 2n-space and its application to the study of the representation theory of the nth complex Weyl algebra A n . The main results are the existence of minimal involutive homogeneous varieties of any g

Diophantine Approximation with Algebraic
Diophantine Approximation with Algebraic Points of Bounded Degree
✍ Min Ru; Julie Tzu-Yueh Wang 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 158 KB

In this paper, we extend Schmidt's subspace theorem to the approximation of algebraic numbers by algebraic points of bounded degree. 2000 Academic Press 1. INTRODUCTION This paper deals with the Diophantine approximation with algebraic points of bounded degree. In 1955, Roth proved his celebrated th

Generalized Cocycles with Values in One-
Generalized Cocycles with Values in One-Units of Henselian Valued Division Algebras
✍ Patrick J. Morandi; B.A. Sethuraman 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 155 KB

Let ZrF be an inertial Galois extension of Henselian valued fields, and let D be a Z-central division algebra. Let G be a finite group acting on Z with fixed field F. We show that every generalized cocycle of G with values in the one-units Ž . of D is cohomologous to one of the form , 1 , or in othe