What the study found
The authors show that the super Jordan plane is super-prime and has a super-simple superartinian ring of fractions. They also compute its groups of superalgebra automorphisms and braided Hopf algebra automorphisms.
Why the authors say this matters
The study suggests these algebraic properties help characterize the super Jordan plane. The authors also note that their approach relies on embedding the Jordan plane as a subalgebra of the super Jordan plane.
What the researchers tested
The paper studies algebraic properties of the super Jordan plane, an algebraic structure introduced by I. Angiono, I. Heckenberger, and the first named author. The authors use an embedding of the Jordan plane as a subalgebra of the super Jordan plane as a key part of their approach.
What worked and what didn't
The authors report that the super Jordan plane is super-prime and that its ring of fractions is super-simple and superartinian. They also determine the automorphism groups mentioned in the abstract.
What to keep in mind
The abstract does not describe detailed proofs, experimental limitations, or broader applications. The summary here is limited to the properties and methods explicitly stated in the abstract.
Key points
- The super Jordan plane is shown to be super-prime.
- Its ring of fractions is described as super-simple and superartinian.
- The authors compute groups of superalgebra automorphisms and braided Hopf algebra automorphisms.
- The Jordan plane is embedded as a subalgebra and used in the authors' approach.
Disclosure
- Research title:
- Super Jordan plane is shown to be super-prime
- Image credit:
- Photo by svetlanabar on Pixabay
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