2010/08/11 by Murray R. Bremner, Bremner, Murray R.
Mathematics · Physics and Astronomy · #16K20 #16S34 #16Z05 #20M20 #20M25 #20M30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 16-02. Secondary 16G10 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math-ph #math.MP #math.RA #math.RT #msc:16-02. #msc:16G10 #msc:16K20 #msc:16S34 #msc:16Z05 #msc:20M20 #msc:20M25 #msc:20M30
paper · pdf · doi:10.48550/arxiv.1008.2006
14 pages, 9 tables
arxiv created 2010/08/11 · openalex publication_date 2010/08/11 · arxiv updated 2010/08/13 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
This is a survey paper on algorithms that have been developed during the last\n25 years for the explicit computation of the structure of an associative\nalgebra of finite dimension over either a finite field or an algebraic number\nfield. This constructive approach was initiated in 1985 by Friedl and Ronyai\nand has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos,\nKuronya and Wales. I illustrate these algorithms with the case n = 2 of the\nrational semigroup algebra of the partial transformation semigroup PTn on n\nelements; this generalizes the full transformation semigroup and the symmetric\ninverse semigroup, and these generalize the symmetric group Sn.\n