Polynomial identities of the octonion algebra

Author(s)

Fernando Henry Meirelles

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2014-06-06

Examining board members

Ivan Chestakov; Plamen Emilov Kochloukov; Alexandr Kornev; Lucia Satie Ikemoto Murakami; Irina Sviridova

• Advisor: Ivan Chestakov

Abstract

In this work we find bases for the T Z 32 and T Z 22 graded identities of the octonion algebra. Using the base obtained in the T Z 22 case, we re-obtain a basis for the Z 2 -graded identities of two by two matrices. We also obtained the simultaneously skew and weak identities of the octonions in the category of alternative algebras. In addition we find a basis of identities for the simple Malcev algebra of dimension seven, sl(O). For both skew cases of identities studied we positively show the Shestakov-Zhukavets conjecture: The T -ideal of identities of the octonions coincides with that of the quadratic alternative algebra. (AU)