Representation Theory, Group Rings, and Coding Theory

<p>In this paper, we introduce a method for computing the primitive decomposition of idempotents in any semisimple finite group algebra, utilizing its matrix representations and Wedderburn decomposition. Particularly, we use this method to calculate the examples of the dihedral group algebras $ \mathbb{C}[D_{2n}] $ and generalized quaternion group algebras $ \mathbb{C}[Q_{4m}] $. Inspired by the orthogonality relations of the character tables of these two families of groups, we obtain two sets of trigonometric identities. Furthermore, a group algebra isomorphism between $ \mathbb{C}[D_{8}] $ and $ \mathbb{C}[Q_{8}] $ is described, under which the two complete sets of primitive orthogonal idempotents of these group algebras correspond bijectively.</p>

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Representation Theory, Group Rings, and Coding Theory

Cited by 3 publications

References 11 publications

The weighted dual functionals for the univariate Bernstein basis

The weighted dual functionals for the univariate Bernstein basis

Weighted dual functions for Bernstein basis satisfying boundary constraints

Primitive decompositions of idempotents of the group algebras of dihedral groups and generalized quaternion groups

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