Classification of division gradings on finite-dimensional simple real algebras

Abstract

We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give the classification, up to isomorphism, of (not necessarily division) gradings on such algebras. Linear algebra over the field of two elements plays an interesting role in the proofs.

15 pages. This is the accepted manuscript (it includes the referee's suggestions) of the article published in Linear Algebra and its Applications

References in corpus (2)

• Classification of division gradings on finite-dimensional simple real algebras
• Simple Graded Division Algebras over the Field of Real Numbers

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• Clifford algebras as twisted group algebras and the Arf invariant
• Gradings on associative algebras with involution and real forms of classical simple Lie algebras
• Pauli gradings on Lie superalgebras and graded codimension growth
• Fine gradings and automorphism groups on associative algebras
• Graded-division algebras over arbitrary fields
• Identities and central polynomials of real graded division algebras