English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce a method computing the primitive decomposition ofidempotents of any semisimple finite group algebra based on its matrixrepresentations and Wedderburn decomposition. Particularly, we use this methodto calculate the examples of the dihedral group algebras $\mathbb{C}[D_{2n}]$and generalized quaternion group algebras $\mathbb{C}[Q_{4m}]$. Inspired by theorthogonality relations of the character tables of these two families ofgroups, we obtain two sets of trigonometric identities. Furthermore, a groupalgebra isomorphism between $\mathbb{C}[D_{8}]$ and $\mathbb{C}[Q_{8}]$ isdescribed, under which the two complete sets of primitive orthogonalidempotents of these two group algebras we find correspond to each otherbijectively.

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