Graded-division algebras and Galois extensions

Elduque, A. (Universidad de Zaragoza) ; Kochetov, M.

Resumen: Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division algebras. On the other hand, given a finite abelian group G, any central simple G-graded-division algebra over a field F is determined, thanks to a result of Picco and Platzeck, by its class in the (ordinary) Brauer group of F and the isomorphism class of a G-Galois extension of F. This connection is used to classify the simple G-Galois extensions of F in terms of a Galois field extension L/F with Galois group isomorphic to a quotient G/K and an element in the quotient Z2(K, L×)/B2(K, F×) subject to certain conditions. Non-simple G-Galois extensions are induced from simple T-Galois extensions for a subgroup T of G. We also classify finite-dimensional G-graded-division algebras and, as an application, finite G-graded-division rings.

Idioma: Inglés

DOI: 10.1016/j.jpaa.2021.106773

Año: 2021

Publicado en: JOURNAL OF PURE AND APPLIED ALGEBRA 225, 12 (2021), 106773 [34 pp.]
ISSN: 0022-4049

Factor impacto JCR: 0.834 (2021)

Categ. JCR: MATHEMATICS rank: 200 / 333 = 0.601 (2021) - Q3 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 220 / 267 = 0.824 (2021) - Q4 - T3

Factor impacto CITESCORE: 1.5 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.866 - Algebra and Number Theory (Q1)

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P
Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-17R

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Algebra (Dpto. Matemáticas)