Mathematics – Rings and Algebras
Scientific paper
2009-07-10
Comm. Algebra 39 (2011) no. 2, 497--520
Mathematics
Rings and Algebras
22 pages; v2: Example 4 corrected; v3: final version, to appear in Comm. Algebra
Scientific paper
We study a noncommutative generalization of Jordan algebras called Jordan dialgebras. These are algebras that satisfy the identities $[x_1 x_2]x_3= 0$, $(x_1^2,x_2,x_3)=2(x_1,x_2,x_1x_3)$, $x_1(x_1^2 x_2)=x_1^2(x_1 x_2)$; they are related with Jordan algebras in the same way as Leibniz algebras are related to Lie algebras. We present an analogue of the Tits---Kantor---Koecher construction for Jordan dialgebras that provides an embedding of such an algebra into Leibniz algebra.
Gubarev Vsevolod Yu.
Kolesnikov Pavel S.
No associations
LandOfFree
The Tits--Kantor--Koecher construction for Jordan dialgebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Tits--Kantor--Koecher construction for Jordan dialgebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Tits--Kantor--Koecher construction for Jordan dialgebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-164156