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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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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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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: Family replication
Journal of Mathematical Physics, 2004The known link of the division algebras to 10-dimensional spacetime and one leptoquark family is extended to encompass three leptoquark families.
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Algebra and Logic, 2014
It is shown that finite-dimensional division algebras over finitely generated fields do not form rigid rings. Multiplicative groups of such algebras have central automorphisms which do not extend to automorphisms of the algebras themselves.
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It is shown that finite-dimensional division algebras over finitely generated fields do not form rigid rings. Multiplicative groups of such algebras have central automorphisms which do not extend to automorphisms of the algebras themselves.
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Indecomposable division algebras
Communications in Algebra, 1979(1979). Indecomposable division algebras. Communications in Algebra: Vol. 7, No. 8, pp. 791-817.
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Variational algorithms for linear algebra
Science Bulletin, 2021Xiaosi Xu, Jinzhao Sun, Suguru Endo
exaly
1982
The first examples of division algebras that were found after the quaternions belong to the class of cyclic division algebras. This class still plays a major role in the theory of central simple algebras. If is a local field, an algebraic number field, or more generally a global field, then every central division algebra over F is cyclic.
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The first examples of division algebras that were found after the quaternions belong to the class of cyclic division algebras. This class still plays a major role in the theory of central simple algebras. If is a local field, an algebraic number field, or more generally a global field, then every central division algebra over F is cyclic.
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1982
In this paper we give a geometrical method for the construction of commutative finite dimensional division algebras over a field K with char K ≠ 2.
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In this paper we give a geometrical method for the construction of commutative finite dimensional division algebras over a field K with char K ≠ 2.
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