Regular representations of semisimple algebras, separable field extensions, group characters, generalized circulants, and generalized cyclic codes

DOI10.1016/0024-3795(93)00167-XzbMath0839.20015MaRDI QIDQ1805200

David Chillag

Publication date: 12 June 1995

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

zbMATH Keywords

partitionssubalgebrasseparable field extensionssemisimple algebrasgroup charactersgeneralized cyclic codes

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Separable extensions, Galois theory (12F10) Cyclic codes (94B15) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (21)

A transform approach to polycyclic and serial codes over rings ⋮ Algorithms for finding the minimal polynomials and inverses of resultant matrices ⋮ Norms and spread of the Fibonacci and Lucas RSFMLR circulant matrices ⋮ Efficient algorithm for finding the inverse and the group inverse of FLS \(r\)-circulant matrix ⋮ Regular representations of finite-dimensional separable semisimple algebras and Gröbner bases ⋮ On the determinants of some kinds of circulant-type matrices with generalized number sequences ⋮ On a congruence of Blichfeldt concerning the order of finite groups ⋮ The Explicit Inverses of CUPL-Toeplitz and CUPL-Hankel Matrices ⋮ Exact determinants of some special circulant matrices involving four kinds of famous numbers ⋮ Fast algorithms for solving FLS \(R\)-factor block circulant linear systems and inverse problem of \(\mathcal{A} X = b\) ⋮ Isomorphic operators and functional equations for the skew-circulant algebra ⋮ Explicit determinants of the RFP\(r\)L\(r\)R circulant and RLP\(r\)F\(r\)L circulant matrices involving some famous numbers ⋮ Algorithms for finding inverse of two patterned matrices over \(\mathbb{Z}_p\) ⋮ Irreducible constituents of monomial representations. ⋮ Skew cyclic displacements and inversions of two innovative patterned matrices ⋮ Polycyclic codes as invariant subspaces ⋮ Primitive normal matrices and covering numbers of finite groups. ⋮ Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices ⋮ Semisimple commutative algebras with positive bases ⋮ Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space ⋮ \(p(x)\)-circulants over finite fields and probability methods of their construction

Cites Work

• Generalized circulants and class functions of finite groups
• Generalized circulants and class functions of finite groups. II
• Nonnegative matrices, Brauer characters, normal subsets, and powers of representation modules
• Shorter Notes: Character Values of Finite Groups as Eigenvalues of Nonnegative Integer Matrices
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