Irreducible characters of wreath products in reality-based algebras and applications to association schemes.

DOI10.1016/J.JALGEBRA.2014.04.009zbMath1315.20005OpenAlexW2051908468MaRDI QIDQ403599

Harvey I. Blau, Bangteng Xu

Publication date: 29 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.04.009

zbMATH Keywords

finite groupsassociation schemeswreath productsirreducible characterscharacter tables\(C\)-algebrasreality-based algebrastable algebras

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Association schemes, strongly regular graphs (05E30) Ordinary representations and characters (20C15) Extensions, wreath products, and other compositions of groups (20E22)

Cites Work

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• Characterizations of wreath products of one-class association schemes
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• Characters of table algebras and applications to association schemes
• Terwilliger algebras of wreath products of one-class association schemes
• Table algebras
• Coherent algebras
• Irreducible representations of wreath products of association schemes
• Erratum: Quotient structures in \(C\)-algebras
• Generalized table algebras
• Direct Products of Association Schemes and Tensor Products of Table Algebras
• Reality-Based Algebras, Generalized Camina-Frobenius Pairs, and the Nonexistence of Degree Maps
• On table algebras, c-algebras, and applications to finite group theory^∗
• Theory of Association Schemes
• Standard integral table algebras generated by a non-real element of small degree

Related Items (14)

Generalized wreath products of table algebras determined by their character tables and applications to association schemes ⋮ The recognition problem for table algebras and reality-based algebras ⋮ Wedge-direct sums of table algebras and applications to association schemes. II ⋮ Quotient structures, homomorphisms, and partial wreath products in reality-based algebras ⋮ Self‐dual association schemes, fusions of Hamming schemes, and partial geometric designs ⋮ Wedge-direct sums of table algebras and applications to association schemes, I ⋮ Noncommutative reality-based algebras of rank 6 ⋮ Structures of commutative table algebras determined by their character tables and applications to finite groups ⋮ On \(p\)-standard table algebras of order \(p^3\) ⋮ Wedge-direct sums of group algebras of finite groups ⋮ Combinatorial extensions of Terwilliger algebras and wreath products of association schemes ⋮ Varietal Terwilliger algebras arising from wreath products of rank two association schemes ⋮ Table algebras with central fusions ⋮ Camina triples and the wedge product of association schemes

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