17 citations · 44 across the 21 of their papers we have counts for
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Factorizations of group determinant in group algebra for any abelian subgroup
Naoya Yamaguchi
We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finit…
Capelli elements of the group algebra
Naoya Yamaguchi
Inspired by the Capelli identities for group determinants obtained by Tôru Umeda, we give a basis of the center of the group algebra of any finite group by using Capelli identities…
Generalization of Frobenius' theorem for group determinants
Naoya Yamaguchi
Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobe…
Proof of some properties of transfer using noncommutative determinants
Naoya Yamaguchi
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by usi…
An extension and a generalization of Dedekind's theorem
Naoya Yamaguchi
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem.…
Compositions of invertibility preserving maps for some monoids and their application to Clifford algebras
Naoya Yamaguchi, Yuka Yamaguchi
For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensiona…