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<p>Let <i>K</i> be an algebraically closed field of characteristic zero, and let <i>A</i> and <i>B</i> be two simple algebras with involution over <i>K</i>. In this note, we study the embedding problem for algebras with involution. More specifically, if the algebra <i>A</i> satisfies the polynomial identities with involution of the algebra <i>B</i>, we investigate whether there exists an embedding of <i>A</i> into <i>B</i> that preserves the involutions.</p>

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The embedding problem in algebras with involution

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Jonatan Andres Gomez Parada

摘要

Let K be an algebraically closed field of characteristic zero, and let A and B be two simple algebras with involution over K. In this note, we study the embedding problem for algebras with involution. More specifically, if the algebra A satisfies the polynomial identities with involution of the algebra B, we investigate whether there exists an embedding of A into B that preserves the involutions.