Relevant bibliographies by topics / Cayley-Dickson Constructing

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  2. Dissertations / Theses

Academic literature on the topic 'Cayley-Dickson Constructing'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Cayley-Dickson Constructing"

1

Korniłowicz, Artur. "Cayley-Dickson Construction." Formalized Mathematics 20, no. 4 (2012): 281–90. http://dx.doi.org/10.2478/v10037-012-0034-9.

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Summary Cayley-Dickson construction produces a sequence of normed algebras over real numbers. Its consequent applications result in complex numbers, quaternions, octonions, etc. In this paper we formalize the construction and prove its basic properties.
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2

Petersson, Holger P. "The non-orthogonal Cayley–Dickson construction and the octonionic structure of the E8-lattice." Journal of Algebra and Its Applications 16, no. 12 (2017): 1750230. http://dx.doi.org/10.1142/s0219498817502309.

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Using a conic [Formula: see text] algebra [Formula: see text] over an arbitrary commutative ring, a scalar [Formula: see text] and a linear form [Formula: see text] on [Formula: see text] as input, the non-orthogonal Cayley–Dickson construction produces a conic algebra [Formula: see text] and collapses to the standard (orthogonal) Cayley–Dickson construction for [Formula: see text]. Conditions on [Formula: see text] that are necessary and sufficient for [Formula: see text] to satisfy various algebraic properties (like associativity or alternativity) are derived. Sufficient conditions guarantee
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3

Cowles, John, and Ruben Gamboa. "The Cayley-Dickson Construction in ACL2." Electronic Proceedings in Theoretical Computer Science 249 (May 2, 2017): 18–29. http://dx.doi.org/10.4204/eptcs.249.2.

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4

PUMPLÜN, S. "A NON-ORTHOGONAL CAYLEY–DICKSON DOUBLING." Journal of Algebra and Its Applications 05, no. 02 (2006): 193–99. http://dx.doi.org/10.1142/s0219498806001697.

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Let R be an integral domain in which 2 is not an invertible element, with quotient field K of characteristic not 2. A construction method for octonion algebras over Ris presented for which the resulting algebra does not necessarily contain a composition subalgebra.
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5

Markov, V. T., and A. A. Tuganbaev. "Cayley–Dickson process and centrally essential rings." Journal of Algebra and Its Applications 18, no. 12 (2019): 1950229. http://dx.doi.org/10.1142/s0219498819502293.

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We describe associative center [Formula: see text] and the center [Formula: see text] of the ring [Formula: see text] obtained by applying the generalized Cayley–Dickson construction and we find conditions under which the ring [Formula: see text] is [Formula: see text]-essential or centrally essential. The obtained results are applied to generalized quaternion rings and octonion rings; we use them to construct an example of a nonassociative centrally essential ring.
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6

Markov, V. T., and A. A. Tuganbaev. "Cayley–Dickson process and centrally essential rings." Journal of Algebra and Its Applications 19, no. 05 (2019): 2050096. http://dx.doi.org/10.1142/s0219498820500966.

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We describe associative center [Formula: see text] and the center [Formula: see text] of the ring [Formula: see text] obtained by applying the generalized Cayley–Dickson construction and we find conditions under which the ring [Formula: see text] is [Formula: see text]-essential or centrally essential. The obtained results are applied to generalized quaternion rings and octonion rings; we use them to construct an example of a nonassociative centrally essential ring.
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7

KINYON, MICHAEL K., J. D. PHILLIPS, and PETR VOJTĚCHOVSKÝ. "C-LOOPS: EXTENSIONS AND CONSTRUCTIONS." Journal of Algebra and Its Applications 06, no. 01 (2007): 1–20. http://dx.doi.org/10.1142/s0219498807001990.

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C-loops are loops satisfying the identity x(y · yz) = (xy · y)z. We develop the theory of extensions of C-loops, and characterize all nuclear extensions provided the nucleus is an abelian group. C-loops with central squares have very transparent extensions; they can be built from small blocks arising from the underlying Steiner triple system. Using these extensions, we decide for which abelian groups K and Steiner loops Q there is a nonflexible C-loop C with center K such that C/K is isomorphic to Q. We discuss possible orders of associators in C-loops. Finally, we show that the loops of signe
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8

Kraußhar, Rolf Sören. "Function Theories in Cayley-Dickson Algebras and Number Theory." Milan Journal of Mathematics, March 8, 2021. http://dx.doi.org/10.1007/s00032-021-00325-y.

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AbstractIn the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford algebras to non-associative Cayley-Dickson algebras, starting with the octonions.An important question is whether there appear really essentially different features in the treatment with Cayley-Dickson algebras that cannot be handled in the Clifford analysis setting. Here we give one concrete example: Cayley-Dickson algebras admit the construction of direct analogues of so-called CM-lattices, in particular, lattices that are closed under multipli
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Dissertations / Theses on the topic "Cayley-Dickson Constructing"

1

Santos, Davi José dos. "A álgebra dos complexos/quatérnios/octônios e a construção de Cayley-Dickson." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/6596.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-12-15T15:01:25Z No. of bitstreams: 2 Dissertação - Davi José dos Santos - 2016.pdf: 5567090 bytes, checksum: 5606aa47f640cc5cd4495d2694f38cda (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-12-15T17:28:21Z (GMT) No. of bitstreams: 2 Dissertação - Davi José dos Santos - 2016.pdf: 5567090 bytes, checksum: 5606aa47f640cc5cd4495d2694f38cda (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made availab
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2

McLewin, Kelly English. "Octonions and the Exceptional Lie Algebra g_2." Thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/9878.

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We first introduce the octonions as an eight dimensional vector space over a field of characteristic zero with a multiplication defined using a table. We also show that the multiplication rules for octonions can be derived from a special graph with seven vertices call the Fano Plane. Next we explain the Cayley-Dickson construction, which exhibits the octonions as the set of ordered pairs of quaternions. This approach parallels the realization of the complex numbers as ordered pairs of real numbers. The rest of the thesis is devoted to following a paper by N. Jacobson written in 1939 entitled "
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