45 citations · 146 across the 27 of their papers we have counts for
5 papers · 1 filter
Classification of the algebras
Marie Kreusch, Sophie Morier-Genoud
We study a series of real nonassociative algebras introduced in . These algebras have a natural -grading, where , and they are charac…
New solutions to the Hurwitz problem on square identities
Anna Lenzhen, Sophie Morier-Genoud, Valentin Ovsienko
The Hurwitz problem of composition of quadratic forms, or of "sum of squares identity" is tackled with the help of a particular class of -graded non-associative a…
Universal Enveloping Algebras of Lie Antialgebras
Séverine Leidwanger, Sophie Morier-Genoud
Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its pro…
Simple graded commutative algebras
Sophie Morier-Genoud, Valentin Ovsienko
We study the notion of -graded commutative algebra for an arbitrary abelian group . The main examples are the Clifford algebras already treated by Albuquerque and Majid. We p…
Well, Papa, can you multiply triplets?
Sophie Morier-Genoud, Valentin Ovsienko
We show that the classical algebra of quaternions is a commutative -graded algebra. A similar interpretation of the algebra of octonions is impossible.