The algebraic and geometric classification of nilpotent noncommutative Jordan algebras. (English) Zbl 1514.17003
The paper contains algebraic (i.e., list of algebras up to isomorphism) and geometric (i.e, description of the corresponding variety) classification of 4-dimensional nilpotent noncommutative Jordan algebras over the field of complex numbers. There are 18 non-isomorphic algebras, and the corresponding variety is the union of \(\mathrm{GL}_4(\mathbb C)\)-orbits of 3 rigid algebras, and two one-parametric families. The classification is done via the standard inductive method of computation of central extensions of algebras of lower dimension.
Reviewer: Pasha Zusmanovich (Ostrava)
MSC:
| 17A15 | Noncommutative Jordan algebras |
References:
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