superalgebra and (synthetic ) supergeometry
A Jordan superalgebra is the analog of a Jordan algebra in superalgebra/supergeometry. A Jordan superalgebra is a -graded algebra , where is a Jordan algebra and a -bimodule with a “Lie-like” product into .
Elements of are supercommutative, that is, , and satisfy the super Jordan identity.
Simple Jordan superalgebras over an algebraically closed field of characteristic 0 were classified by Kac (Kac 77). The only exceptional finite-dimensional example is the 10-dimensional Jordan superalgebra .
Victor Kac, Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5(1977), 1375–1400, (doi: 10.1080/00927877708822224)
Isaiah Kantor, Connections between Poisson brackets and Jordan and Lie superalgebras, Lie theory, differential equations and representation theory, Montreal (1989), 213–225.
Irving Kaplansky, Graded Jordan algebras I (preprint).
Consuelo Martínez, Simplicity of Jordan Superalgebras and Relations with Lie Structures, Irish Math. Soc. Bulletin 50(2003), 97–116 (pdf)
M. E. Martin, Classification of three-dimensional Jordan superalgebras (arXiv:1708.01963)
Last revised on July 8, 2020 at 07:11:44. See the history of this page for a list of all contributions to it.