摘要 : Let F be an algebraically closed field of characteristic zero and let G be a finite group. Consider G-graded simple algebras A which are finite dimensional and e-central over F, i.e. Z(A)(e) := Z(A)boolean AND A(e) = F. For any su... 展开 Let F be an algebraically closed field of characteristic zero and let G be a finite group. Consider G-graded simple algebras A which are finite dimensional and e-central over F, i.e. Z(A)(e) := Z(A)boolean AND A(e) = F. For any such algebra we construct a generic G-graded algebra U which is Azumaya in the following sense. (1) (Correspondence of ideals): There is one to one correspondence between the G-graded ideals of U and the ideals of the ring R, the e-center of U. (2) Artin-Procesi condition: U satisfies the G-graded identities of A and no nonzero G-graded homomorphic image of U satisfies properly more identities. (3) Generic: If B is a G-graded algebra over a field then it is a specialization of U along an ideal a is an element of spec(Z(U)(e)) if and only if it is a G-graded form of A over its e-center.We apply this to characterize finite dimensional G-graded simple algebras over F that admit a G-graded division algebra form over their e-center. (C) 2022 Elsevier Inc. All rights reserved. 收起