Abstract.
Let A be a central simple algebra of degree n over a field of characteristic different from 2 and let B ? A be a maximal commutative subalgebra. We show that if there is an involution on A that preserves B and such that the socle of each local component of B is a homogeneous C 2 -module for this action, then B is a Frobenius algebra.
For a fixed commutative Frobenius algebra B of finite dimension n equipped with an involution σ, we characterize the central simple algebras A of degree n that contain B and carry involutions extending σ.
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Received: 29 October 2001 / Revised version: 2 February 2002
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Chuard-Koulmann, P., Morales, J. Extending involutions on Frobenius algebras. Manuscripta Math. 108, 439–451 (2002). https://doi.org/10.1007/s002290200276
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DOI: https://doi.org/10.1007/s002290200276