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Valuations on Algebraic Division Algebras
Communications in Algebra, 2017ABSTRACTLet D be a division algebra algebraic over its center F. Given a (Krull) valuation v on F, it is shown that v extends to a valuation on D if and only if for each separable element c∈D′ there exists a valuation w on K: = F(c) extending v on F such that K∩D′⊂W∗, where D′ is the derived group of D* and W* is the unit group of the valuation ring W ...
R. Fallah-Moghaddam, M. Mahdavi-Hezavehi
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Division Algebras, Clifford Algebras, Periodicity
Advances in Applied Clifford Algebras, 2018Periodicities in Clifford algebra theory of orders \(2,4,\) and \(8\) are well known. Starting from a result from lattice theory, in which a \(24\)-dimensional Leech lattice can be represented in the \(3\)-dimensional space with octonion components, the main goal of this paper is to prove that, by exploiting the octonion algebra, in Clifford algebra ...
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Real Commutative Division Algebras
Algebras and Representation Theory, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Darpö, Erik, Dieterich, Ernst
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Canadian Journal of Mathematics, 1959
Let K* be an associative algebra over a field F with identity u, and let u, e1, e2, … , be a basis for K*. Denote by K the linear space, over F, spanned by the ei,i = 1, 2, … . Then for x, y in K, xy = αu + a, where a ∈ K. Define h(x, y) = α and x.y = a.
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Let K* be an associative algebra over a field F with identity u, and let u, e1, e2, … , be a basis for K*. Denote by K the linear space, over F, spanned by the ei,i = 1, 2, … . Then for x, y in K, xy = αu + a, where a ∈ K. Define h(x, y) = α and x.y = a.
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Real Flexible Division Algebras
Canadian Journal of Mathematics, 1982In this paper we classify finite-dimensional flexible division algebras over the real numbers. We show that every such algebra is either (i) commutative and of dimension one or two, (ii) a slight variant of a noncommutative Jordan algebra of degree two, or (iii) an algebra defined by putting a certain product on the 3 × 3 complex skew-Hermitian ...
Benkart, Georgia M. +2 more
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On the ζ-Functions of a Division Algebra
The Annals of Mathematics, 1963In this paper, we will develop a theory of C-functions with characters in a division algebra. The ordinary C-function of a division algebra was introduced by K. Hey [4], and generalized by M. Eichler [1] to L-functions with abelian characters. The first attempt to generalize these theories to C-functions with non-abelian characters is due to H.
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On Semi-Automorphisms of Division Algebras
The Annals of Mathematics, 1947Ein Semiautomorphismus eines Ringes \(A\) ist eine eineindeutige Abbildung \(a\to a^S\) von \(A\) auf sich mit \[ (a + b)^S = a^S + b^S \tag{1} \] \[ (ab)^S + (ba)^S = a^Sb^S + b^Sa^S. \tag{2} \] Der Verf. zeigt, daß ein Semiautomorphismus einer halbeinfachen Algebra über einem Körper mit von \(2\) verschiedener Charakteristik entweder ein direkter ...
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On Involutions of Quasi-Division Algebras
Canadian Mathematical Bulletin, 1975All algebras are assumed to be finite dimensional and not necessarily associative. An involution of an algebra is an algebra automorphism of order two. A quasi-division algebra is any algebra in which the non-zero elements form a quasi-group under multiplication.
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The double sign of a real division algebra of finite dimension greater than one
Mathematische Nachrichten, 2012Erik Darpo, Ernst Dieterich
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Division algebra counterexamples of degree 8
Israel Journal of Mathematics, 1981Louis H Rowen, Rowen Louis H
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