|
Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 3, Pages 626–637
(Mi smj2113)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
The Lie algebra of skew-symmetric elements and its application in the theory of Jordan algebras
S. R. Sverchkov Novosibirsk State University, Novosibirsk
Abstract:
We prove that the Lie algebra of skew-symmetric elements of the free associative algebra of rank 2 with respect to the standard involution is generated as a module by the elements $[a,b]$ and $[a,b]^3$, where $a$ and $b$ are Jordan polynomials. Using this result we prove that the Lie algebra of Jordan derivations of the free Jordan algebra of rank 2 is generated as a characteristic $F$-module by two derivations. We show that the Jordan commutator $s$-identities follow from the Glennie–Shestakov $s$-identity.
Keywords:
skew-symmetric element, standard involution, Lie algebra, free associative algebra, Jordan derivation, Jordan $s$-identity.
Received: 02.07.2009
Citation:
S. R. Sverchkov, “The Lie algebra of skew-symmetric elements and its application in the theory of Jordan algebras”, Sibirsk. Mat. Zh., 51:3 (2010), 626–637; Siberian Math. J., 51:3 (2010), 496–506
Linking options:
https://www.mathnet.ru/eng/smj2113 https://www.mathnet.ru/eng/smj/v51/i3/p626
|
Statistics & downloads: |
Abstract page: | 361 | Full-text PDF : | 77 | References: | 66 | First page: | 7 |
|