Menichetti's nonassociative $G$-crossed product algebras
Abstract
We construct unital central nonassociative algebras over a field $F$ which have either an abelian Galois extensions $K/F$ or a central simple algebra over a separable extension of $F$ in their nucleus. We give conditions when these algebras are division algebras. Our constructions generalize algebras studied by Menichetti over finite fields. The algebras are examples of non-trivial semiassociative algebras and thus relevant for the semiassociative Brauer monoid recently defined by Blachar, Haile, Matzri, Rein, and Vishne. When ${\rm Gal}(K/F)=G$ the algebras of the first type can be viewed as nonassociative $G$-crossed product algebras.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.16256
- arXiv:
- arXiv:2407.16256
- Bibcode:
- 2024arXiv240716256P
- Keywords:
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- Mathematics - Rings and Algebras