|
Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 1, Pages 87–111
(Mi smj1170)
|
|
|
|
This article is cited in 7 scientific papers (total in 7 papers)
Jordan (super)coalgebras and Lie (super)coalgebras
V. N. Zhelyabin Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We discuss the question of local finite dimensionality of Jordan supercoalgebras. We establish a connection between Jordan and Lie supercoalgebras which is analogous to the Kantor–Köecher–Tits construction for ordinary Jordan superalgebras. We exhibit an example of a Jordan supercoalgebra which is not locally finite-dimensional. Show that, for a Jordan supercoalgebra $(J,\Delta)$ with a dual algebra $J^*$, there exists a Lie supercoalgebra $(L^c(J),\Delta_L)$ whose dual algebra $(L^c(J))^*$ is the Lie $KKT$-superalgebra for the Jordan superalgebra $J^*$. It is well known that some Jordan coalgebra $J^0$ can be constructed from an arbitrary Jordan algebra $J$. We find necessary and sufficient conditions for the coalgebra $(L^c(J^0),\Delta_L)$ to be isomorphic to the coalgebra $(\operatorname{Loc}(L_{\textup{in}}(J)^0),\Delta^0_L)$, where $L_{\textup{in}}(J)$ is the adjoint Lie $KKT$-algebra for the Jordan algebra $J$.
Keywords:
Jordan superalgebra, Lie superalgebra, Kantor–Köcher–Tits construction, Jordan coalgebra, Lie coalgebra.
Received: 25.02.2002
Citation:
V. N. Zhelyabin, “Jordan (super)coalgebras and Lie (super)coalgebras”, Sibirsk. Mat. Zh., 44:1 (2003), 87–111; Siberian Math. J., 44:1 (2003), 73–92
Linking options:
https://www.mathnet.ru/eng/smj1170 https://www.mathnet.ru/eng/smj/v44/i1/p87
|
Statistics & downloads: |
Abstract page: | 364 | Full-text PDF : | 99 | References: | 66 |
|