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In his remarkable article “Quadratic division algebras” (Trans. Amer. Math. Soc. 105 (1962), 202–221), J. M. Osborn claims to solve ‘the problem of determining all quadratic division algebras of order 4 over an arbitrary field F of characteristic not two . . . modulo the theory of quadratic forms over F ’ (cf. p. 206). While we shall explain in which… (More)

A square-ordered field, also called Hilbert field of type (A), is understood to be an ordered field all of whose positive elements are squares. The problem of classifying, up to isomorphism, all 4-dimensional quadratic division algebras over a square-ordered field k is shown to be equivalent to the problem of finding normal forms for all pairs (X, Y ) of 3×… (More)

- José Antonio Cuenca Mira, Erik Darpö, Ernst Dieterich, José Antonio Cuenca
- 2009

An absolute valued algebra is a non-zero real algebra that is equipped with a multiplicative norm. We classify all finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity, up to algebra isomorphism. This completes earlier results of Ramı́rez Álvarez [24] and Rochdi [25],[26] which, in our self-contained… (More)

- Ernst Dieterich
- 2011

We present a short and rather self-contained introduction to the theory of finite dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In sections 2–3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the… (More)

- Ernst Dieterich
- 2007

By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0, π]. We present a necessary and sufficient criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of… (More)

A dissident map on a finite-dimensional euclidean vector space V is understood to be a linear map η : V ∧V → V such that v, w, η(v∧w) are linearly independent whenever v, w ∈ V are. This notion of a dissident map provides a link between seemingly diverse aspects of real geometric algebra, thereby revealing its shifting significance. While it generalizes on… (More)

- Ernst Dieterich
- 2004

The category of all 2-dimensional real division algebras is shown to split into four full subcategories each of which is given by the natural action of a Coxeter group of type A1 or A2 on the set of all pairs of ellipses in R which are centred in the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions are being… (More)

- Ernst Dieterich
- 2000

Given a euclidean vector space V , a linear map η : V ∧ V → V is called dissident in case v, w, η(v∧w) are linearly independent whenever so are v, w ∈ V . The problem of classifying all real quadratic division algebras is reduced to the problem of classifying all eight-dimensional real quadratic division algebras, and further to the problem of classifying… (More)

- Erik Darpö, Ernst Dieterich
- 2011

For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a ∈ A\{0} are shown to form an invariant of A, called its double sign. For each n ∈ {2, 4, 8}, the double sign causes the category Dn of all n-dimensional real division algebras to decompose into… (More)

- Ernst Dieterich, William Baier, Hermann Doose, Ingrid E. B. Tuxhorn, Helmut Fichsel
- Neuropediatrics
- 1985

The purpose of the follow-up study was to determine whether modern therapy with ethosuximide and/or valproate with/without phenobarbitone and its derivatives improves the longterm prognosis of absence epilepsy as compared to formerly used treatments. The patient population consisted of 194 cases (88 boys, 106 girls) with spike wave epilepsy starting with… (More)