Fixed subalgebra of a commutative Frobenius algebra
Author:
Gorô Azumaya
Journal:
Proc. Amer. Math. Soc. 81 (1981), 213-216
MSC:
Primary 16A36; Secondary 16A72, 16A74
DOI:
https://doi.org/10.1090/S0002-9939-1981-0593459-9
MathSciNet review:
593459
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a finite-dimensional commutative algebra generated by a single element, and let
. We prove that the fixed subalgebra of
under the involution
is Frobenius if and only if either the characteristic of
is different from 2 or
is separable.
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- [2] T. Nakayama and C. J. Nesbitt, Note on symmetric algebras, Ann. of Math. 39 (1938), 659-668. MR 1503430
- [3]
J. L. Pascaud and J. Valette, Group actions on
-
-rings, Proc. Amer. Math. Soc. 76 (1979), 43-44. MR 534387 (80m:16011)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1981-0593459-9
Keywords:
Finite group of automorphisms acting on a ring,
Frobenius algebra,
characteristic different from 2
Article copyright:
© Copyright 1981
American Mathematical Society