Results 51 to 60 of about 93 (80)
Finite Semifields and Projective Planes [PDF]
, 1963 NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This paper makes contributions to the structure theory of finite semifields, i.e., of finite nonassociative division algebras with unit.
Knuth, Donald Ervin
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The coordinate algebra of extended affine Lie algebras of type A(1).
, 1999 In this thesis we classify the coordinate algebra of extended affine Lie algebras, EALA's for short, of type A1. The coordinate algebras of EALA's of the other reduced types were already described in [6], [7] and [2].
Yoshii, Yoji.
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On locally complex algebras and low-dimensional Cayley–Dickson algebras
, 2011 The paper begins with short proofs of classical theorems by Frobenius and (resp.) Zorn on associative and (resp.) alternative real division algebras. These theorems characterize the first three (resp. four) Cayley–Dickson algebras.
Špenko, Špela +5 more
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Determination of division algebras with 243 elements
, 2010 Finite nonassociative division algebras (i.e., finite semifields) with 243 elements are completely ...
I. F. Rúa +2 more
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Octonionic Cayley spinors and $E_6$ [PDF]
, 2010 summary:Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group $E_6$, and of its subgroups. We are therefore led to
Manogue, Corinne A., Dray, Tevian
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Relaxed linear spaces and a generalization of the Cayley–Dickson process
, 2011 In this paper first we introduce a new generalization of vector spaces and linear nonassociative algebras, and then we apply these new concepts to produce new structures related to the classical real division algebras but with dimensions other than 1, 2,
Felipe, Raúl +3 more
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Menichetti\u27s nonassociative $G$-crossed product algebras
We construct unital central nonassociative algebras over a field $F$ which have either an abelian Galois extensions $K/F$ or a central simple algebra over a separable extension of $F$ in their nucleus.
Pumpluen, Susanne
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The automorphisms of differential extensions of characteristic p
Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension K of exponent one of a field F, F of characteristic p, or of a central division algebra over a purely ...
Pumplün, S.
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On Nonassociative Division Rings and Projective Planes
, 2000 An interesting thing happens when one begins with the axioms of a field, but does not require the associative and commutative properties. The resulting nonassociative division ring is referred to as a ``semifield" in this paper.
Landquist, Eric Jon
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On the use of cyclic algebras in lattice-based cryptography
This thesis studies the role of cyclic algebras in lattice-based cryptography. It analyses the security of the mathematical problems underlying a public key encryption (PKE) scheme called CLWE, a variant of Learning with Errors defined over cyclic ...
Mendelsohn, Andrew
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