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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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: 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.


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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

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