September 29, 2025Open Access

Simple Jordan superalgebras with the even parts of Clifford type

Key Points

Only simple infinite dimensional Jordan superalgebras with finite dimensional even parts are the superalgebras of superforms.
The study shows that for even parts of Clifford type, configurations with two summands are impossible.
Results confirm that only one summand in the sums of bilinear forms can occur in these Jordan superalgebras.
This classification provides foundational insights into the structure of infinite dimensional algebraic systems.

Abstract

The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensional Jordan superalgebras with finite dimensional even parts are the superalgebras of superforms. Then we consider the superalgebras whose even parts are infinite dimensional algebras of ``Clifford type'', that is, direct sums of algebras of bilinear forms. The results of RZ show that the number of summonds in these sums is 1 or 2. We prove that the second case is impossible and that the simple infinite dimensional Jordan superalgebras of the first type are the superalgebras of superforms.

Simple Jordan superalgebras with the even parts of Clifford type

Key Points

Abstract

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