arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0907.2047math.RA
收藏

32维Cayley-Dickson代数的子代数结构

The Subalgebra Structure of the Cayley-Dickson Algebra of Dimension 32 (trigintaduonion)

Raoul E. Cawagas, Alexander S. Carrascal, Lincoln A. Bautista, John P. Sta. Maria, Jackie D. Urrutia, Bernadeth Nobles

摘要:

Cayley-Dickson代数R(实数)、C(复数)、H(四元数)、O(八元数)、S(sedenions)和T(trigintaduonions)因其在纯粹数学和理论物理中的重要应用而引起了许多数学家和物理学家的注意。本文通过分析代数T的32个基元所生成的64阶循环T_L,确定了T的子代数结构。分析表明,T_L是一个非结合有限可逆回路(NAFIL),它有373个32,16,8,4,2阶的非平凡子回路,且都是正规的.这些子循环生成T的16、8、4、2和1维的子代数,这些子代数形成了T的结构的元素。

英文摘要:

The Cayley-Dickson algebras R (real numbers), C (complex numbers), H (quaternions), O (octonions), S (sedenions), and T (trigintaduonions) have attracted the attention of several mathematicians and physicists because of their important applications in both pure mathematics and theoretical physics. This paper deals with the determination of the subalgebra structure of the algebra T by analyzing the loop T_L of order 64 generated by its 32 basis elements. The analysis shows that T_L is a non-associative finite invertible loop (NAFIL) with 373 non-trivial subloops of orders 32, 16, 8, 4, and 2 all of which are normal. These subloops generate subalgebras of T of dimensions 16, 8, 4, 2, and 1 which form the elements of its structure.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑