Bulletin of the Australian Mathematical Society· 2026Q2
AN EXPLICIT MATRIX UNIT REALISATION OF THE WEDDERBURN DECOMPOSITION
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- Q2SCImago
- 2026year
Short summary
Researchers constructed explicit group-algebra elements that realize the Wedderburn decomposition of a finite group algebra, yielding an algebra isomorphism identical to the classical Wedderburn isomorphism.
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Key points
- Explicit group-algebra elements are constructed for elementary matrices in the Wedderburn decomposition of finite group algebras.
- These elements yield an explicit algebra isomorphism that matches the classical Wedderburn isomorphism.
- The construction is applied to the symmetric group to compute a transition matrix for the center.
- The Frobenius characteristic map is reinterpreted using the Wedderburn decomposition.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We construct explicit group-algebra elements corresponding to the elementary matrices in the Wedderburn decomposition of a finite group algebra. These elements yield an explicit algebra isomorphism that coincides with the classical Wedderburn isomorphism. As applications, we apply our construction to the symmetric group to compute the transition matrix between two natural bases of the centre and reinterpret the Frobenius characteristic map through the Wedderburn decomposition. Consequently, we show that the Schur basis is naturally compatible with the identity-matrix basis arising from the Wedderburn decomposition.
The authors' abstract, as published at the source. Bulletin of the Australian Mathematical Society, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics