Simple nonassociative alternative superalgebras are classified Any such superalgebra either is trivial (ie, has zero odd part) or has characteristic 2 or 3 and is isomorphic over its center to a superalgebra of one of the following five types: in characteristic 3, these are two superalgebras of dimensions 3 and 6 and a “twisted superalgebra of vector type,” which either is infinite-dimensional or has dimension 2·3n; in characteristic 2, those are either a Cayley-Dixon algebra with a grading induced by the Cayley-Dixon process or a “double Cayley-Dixon algebra” Under certain constraints on the structure of even parts, we also give a description of prime nonassociative alternative nontrivial superalgebras in terms of central orders of simple superalgebras The simple superalgebras of dimensions 3 and 6 are then used to construct simple Jordan superalgebras of characteristic 3 and of dimensions 12 and 21, respectively

Prime alternative superalgebras of arbitrary characteristic

Simple Finite-Dimensional Jordan Superalgebras of Prime Characteristic

Classification of linearly compact simple Jordan and generalized Poisson superalgebras

The problem of speciality and i-speciality is considered for Jordan superalgebras related with Poisson superalgebras. The quantizations of Poisson superalgebras play an important role in the consideration. The i-speciality of Jordan Poisson superalgebras is obtained by means of quantization of Poisson superalgebras. The criterium for speciality of Jordan Poisson superalgebras is given also.

Quantization of poisson superalgebras and speciality of jordan poisson superalgebras

Speciality and non-speciality of two Jordan superalgebras

Superalgebras J(F) of finite or infinite dimension obtained by the Kantor doubling process from dot-bracket superalgebras (F, ., x ) with a supercommutative, associative product . and a superbracket x are examined. Such a superalgebra is Jordan if and only if x is a Jordan superbracket and is simple if and only if (F, ., x) is simple. Superalgebras J(F) of vector type where D is a derivation of (F, .)) are special. Superalgebras J(F) for poisson brackets F on even and odd variables are exceptional except in the case of a single odd variable and no even variables.

King Daniel

Papers

The kantor construction of jordan superalgebras