REMARK ON THE JACOBI IDENTITIES IN ASSOCIATIVE ALGEBRAS

Ivashkina K. S., Lavrov P. M.

Information About Author:

In the paper associative algebras and Jacobi identities, which appear after introduction of commutator and write down in the form of double commutators for arbitrary three elements of a given algebra, are considered. We show that in any associative algebra there exist identities, which are written in the form of single commutators for any three elements. From these identities one can derive the Jacobi identities but not the contrary. It allows us to speak of fundamental (basic) identities existing for any associative algebra.

Keywords: associative algebras, commutator, Jacobi identities, generalized Jacobi identities

( 364.51 kB ) ( 359.45 kB )

Issue: 8, 2013

Series of issue: Issue 8

Rubric: INTERDISCIPLINARY STUDIES

Pages: 198 — 199

Downloads: 868