Quadratic Jordan superpairs covered by grids.
In this paper, the theory of Jordan pairs covered by grids is extended to the super setting in a great generality. Scalars are allowed to belong to an arbitrary commutative associative and unital superring. All the necessary background on supermodules over superrings, as well as on quadratic superforms is provided. Then the basic theory of (quadratic) Jordan superpairs, Jordan supertriples and unital Jordan superalgebras over superrings is developed. Many examples are provided too. Grids and refined root gradings are introduced for Jordan superpairs and the classification of Jordan superpairs covered by a grid is given, thus extending to the super setting the results obtained previously by the author \textit{E.~Neher} [Am. J. Math. 118, 439--491 (1996; Zbl 0857.17019)]. Moreover, the description of refined root gradings is provided too, this being new even in the ungraded case.
scientific article; zbMATH DE number 2005900
scientific article