On Jordan bases for the tensor product and Kronecker sum and their elementary divisors over fields of prime characteristic

DOI10.1080/03081080701395640zbMath1146.15018OpenAlexW1990566969MaRDI QIDQ3518583

C. W. Norman

Publication date: 8 August 2008

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081080701395640

zbMATH Keywords

Kronecker productKronecker sumtensor productGreen ringcompanion matricesJordan bases\(p\)-adic expansionfields of prime characteristicJordan block matricesmultiplicities of elementary divisors

Mathematics Subject Classification ID

Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Multilinear algebra, tensor calculus (15A69) Canonical forms, reductions, classification (15A21)

Related Items (11)

The Loewy length of a tensor product of modules of a dihedral two-group. ⋮ Exterior and symmetric powers of modules for cyclic 2-groups. ⋮ Adjoint Jordan blocks for simple algebraic groups of type \(C_{\ell}\) in characteristic two ⋮ Decomposing modular tensor products, and periodicity of `Jordan partitions' ⋮ Is every matrix similar to a polynomial in a companion matrix? ⋮ Generators for decompositions of tensor products of modules associated with standard Jordan partitions ⋮ Generators for decompositions of tensor products of modules. ⋮ On the elementary divisors of the Sylvester and Lyapunov maps ⋮ Jordan blocks of nilpotent elements in some irreducible representations of classical groups in good characteristic ⋮ Decomposition of exterior and symmetric squares in characteristic two ⋮ Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Cites Work

• Combinatorial verification of the elementary divisors of tensor products
• On Jordan bases for two related linear mappings
• A canonical basis for the matrix transformation \(X \to AX+XB\)
• A canonical basis for the matrix transformation \(X\to AXB\)
• How to compute the elementary divisors of the tensor product of two matrices
• Elementary divisors of tensor products
• On direct product matrices
• The Normal Form of Compound and Induced Matrices
• On the jordan form of the tensor product over fields of prime characteristic
• Decomposition of Products of Modular Representations
• The Modular Representation Ring of a Cyclic p -Group
• On Induced and Compound Matrices

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