Bimodule-valued hermitian and quadratic forms
Let \(k\) be a commutative ring and \(A\) a unital associative \(k\)-algebra. The author introduces the notion of a hermitian form with values in a \((A\)-\(A^{op})\)-bimodule \(L\). The notion of a form parameter, as introduced by Bak, appears as the special case where \(L\) is an invertible \((A\)-\(A^{op})\)-bimodule which is free on one generator as a right \(A\)- module. The main result is that \(L\)-valued forms, with \(L\) invertible, occur naturally in the categorical setting of \textit{H. Quebbemann}, \textit{W. Scharlau} and \textit{M. Schulte} [J. Algebra 59, 264-289 (1979; Zbl 0412.18016)]. They are the hermitian and quadratic forms (in this categorical setting) on the category of finitely generated projective \(A\)-modules.
scientific article; zbMATH DE number 743515