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*-algebra
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, and more specifically in <a href="/facts/Abstract_algebra/YNNE1CNz">abstract algebra</a>, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an <a href="/facts/Associative_algebra/DRfoF6KV">associative algebra</a> over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the <a href="/facts/Complex_numbers/2w7mqI7e">complex numbers</a> and <a href="/facts/Complex_conjugation/7TEaoQDe">complex conjugation</a>, <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrices</a> over the complex numbers and <a href="/facts/Conjugate_transpose/7eBWtqVG">conjugate transpose</a>, and <a href="/facts/Linear_operator/Q1PBKNVV">linear operators</a> over a <a href="/facts/Hilbert_space/aDFMh4lV">Hilbert space</a> and <a href="/facts/Hermitian_adjoint/gN6RHphd">Hermitian adjoints</a>. However, it may happen that an algebra admits no <a href="/facts/Involution_(mathematics)/kKxYrUVa">involution</a>. </p> Look up <i>*</i> or <i>star</i> in Wiktionary, the free dictionary.