The <i>kS</i>₃-Module Algebra Structures on <i>M</i>₃(<i>k</i>)

Abstract

Let S 3 be the symmetric group on three elements. Let k be a field and M 3 ( k ) be the full matrix algebra of 3 × 3 -matrices over k. In this paper, the k S 3 -module algebra structures on M 3 ( k ) are described, and classified up to isomorphism.

Keywords

• matrix algebra
• module algebra
• weak similarity
• Hopf algebra
• group algebra