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1.
With the newly developed octonion analytic function theory, we confirm the octonionic analogue of the Calderón's conjecture. As application, we obtain the Plemelj formula in octonionic space. 相似文献
2.
Abstract We identify ℝ7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for
the unit sphere S6. It is known that a cone over a surface M in S6 is an associative submanifold of ℝ7 if and only if M is almost complex in S6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S6 are the equation for primitive maps associated to the 6-symmetric space G2=T2, and use this to explain some of the known results. Moreover, the equation for S1-symmetric almost complex curves in S6 is the periodic Toda lattice, and a discussion of periodic solutions is given.
(Dedicated to the memory of Shiing-Shen Chern)
* Partially supported by NSF grant DMS-0529756. 相似文献
3.
We prove that the octonionic polynomials V ■k l 1 ··· l k are independent of the associative orders ■k . This improves the octonionic Taylor type theorem. 相似文献
4.
Given a field F and integer n≥3, we introduce an invariant sn (F) which is defined by examining the vanishing of subspaces of alternating bilinear forms on 2-dimensional subspaces of vector spaces. This invariant arises when we calculate the largest dimension of a subspace of n?×?n skew-symmetric matrices over F which contains no elements of rank 2. We show how to calculate sn (F) for various families of field F, including finite fields. We also prove the existence of large subgroups of the commutator subgroup of certain p-groups of class 2 which contain no non-identity commutators. 相似文献
5.
Chuu-Lian TERNG 《数学年刊B辑(英文版)》2006,27(2)
We identify R7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S6. It is known that a cone over a surface M in S6 is an associative submanifold of R7 if and only if M is almost complex in S6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S6 are the equation for primitive maps associated to the 6-symmetric space G2/T2, and use this to explain some of the known results. Moreover, the equation for S1-symmetric almost complex curves in S6 is the periodic Toda lattice, and a discussion of periodic solutions is given. 相似文献
6.
Paul Boddington Dmitriy Rumynin 《Proceedings of the American Mathematical Society》2007,135(6):1651-1657
We prove a stronger version of Curtis' classification theorem of finite subloops of the Cayley octonions .
7.
S. Madariaga 《代数通讯》2013,41(3):1009-1018
The purpose of this brief note is to prove that any coassociative bialgebra deformation of the universal enveloping algebra of the seven dimensional central simple exceptional Malcev algebra over a field of characteristic zero is cocommutative. 相似文献
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9.
《复变函数与椭圆型方程》2012,57(13):1031-1040
It is shown that there is only one possible way to define the O-analytic functions. A simple way to construct the O-analytic functions is also given. 相似文献
10.
In this paper, we give an algorithm to find the roots of the octonionic quadratic equation x 2 + bx + c = 0, and develop a Matlab package to find solutions. We also discuss how to find the roots of some other octonion quadratic equations, such as an algorithm is given for finding the roots of the octonion quadratic equation xax + bx + c = 0. 相似文献