How to compute the Wedderburn decomposition of a finite-dimensional associative algebra

DOI10.1515/gcc.2011.003zbMath1250.16018arXiv1008.2006OpenAlexW2962884332MaRDI QIDQ2882824

Murray R. Bremner

Publication date: 7 May 2012

Published in: Groups – Complexity – Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.2006

zbMATH Keywords

algorithmsmatrix algebrasrepresentationsradicalstransformation semigroupsWedderburn decompositionsfinite-dimensional associative algebras

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Semigroups of transformations, relations, partitions, etc. (20M20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Representations of associative Artinian rings (16G10) Semigroup rings, multiplicative semigroups of rings (20M25) Finite-dimensional division rings (16K20) Computational aspects of associative rings (general theory) (16Z05) Software, source code, etc. for problems pertaining to associative rings and algebras (16-04) Representation of semigroups; actions of semigroups on sets (20M30)

Related Items (8)

Cryptographic algorithms on groups and algebras ⋮ Jordan quadruple systems ⋮ Primitive orthogonal idempotents for \(R\)-trivial monoids. ⋮ Exact hierarchical reductions of dynamical models via linear transformations ⋮ Splitting full matrix algebras over algebraic number fields. ⋮ Structure of the rational monoid algebra for Boolean matrices of order 3 ⋮ Special identities for comtrans algebras ⋮ Universal Associative Envelopes of Nonassociative Triple Systems

Cites Work

• Decompositions of algebras over \(\mathbb{R}\) and \(\mathbb{C}\)
• Decomposition of algebras over finite fields and number fields
• Finding the radical of an algebra of linear transformations
• Efficient decomposition of associative algebras over finite fields
• Joseph H. M. Wedderburn and the structure theory of algebras
• On the irreducible representations of a finite semigroup
• Complex Representations of Finite Monoids

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