Fixed subalgebra of a commutative Frobenius algebra
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- by Gorô Azumaya PDF
- Proc. Amer. Math. Soc. 81 (1981), 213-216 Request permission
Abstract:
Let $B$ be a finite-dimensional commutative algebra generated by a single element, and let $A = B \otimes B$. We prove that the fixed subalgebra of $A$ under the involution ${b_1} \otimes {b_2} \mapsto {b_2} \otimes {b_1}$ is Frobenius if and only if either the characteristic of $B$ is different from 2 or $B$ is separable.References
- Tadasi Nakayama, On Frobeniusean algebras. II, Ann. of Math. (2) 42 (1941), 1–21. MR 4237, DOI 10.2307/1968984
- Tadasi Nakayama and Cecil Nesbitt, Note on symmetric algebras, Ann. of Math. (2) 39 (1938), no. 3, 659–668. MR 1503430, DOI 10.2307/1968640
- J.-L. Pascaud and J. Valette, Group actions on Q-F-rings, Proc. Amer. Math. Soc. 76 (1979), no. 1, 43–44. MR 534387, DOI 10.1090/S0002-9939-1979-0534387-5
Additional Information
- © Copyright 1981 American Mathematical Society
- 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