Universal R-matrices for finite Abelian groups -- a new look at graded multilinear algebra

1995/08/24 by M. Scheunert, Scheunert, M.
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9508016

openalex publication_date 1995/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The universal R-matrices and, dually, the coquasitriangular structures of the group Hopf algebra of a finite Abelian group (resp. of an arbitrary Abelian group) are determined. This is used to formulate graded multilinear algebra in terms of triangular or cotriangular Hopf algebras. For the convenience of the reader, in a separate section the definitions and basic properties of quasitriangular and coquasitriangular Hopf algebras are recalled.

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