Extending involutions on Frobenius algebras |
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| Authors: | Pascale Chuard-Koulmann Jorge Morales |
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| Institution: | (1) Institut de Mathématiques, Université de Neuchatel, Rue Emile Argand 11, CH-2007 Neuchatel, Switzerland. e-mail: pascale.chuard@maths.unine.ch, CH;(2) Department of Mathematics, Louisiana State University, Baton Rouge, LA 70808, USA. e-mail: morales@math.lsu.edu, US |
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| 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.
Received: 29 October 2001 / Revised version: 2 February 2002 |
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