Twisted Kähler differential forms (Q1812024)

Let \(A\) be an associative algebra with an endomorphism \(\alpha\). The authors construct a twisted analogue \(\Omega^\bullet A\) of the differential graded algebra of Kähler differential forms by imposing relations \((da)b=(\alpha b)(da)\) for \(a,b\in A\). Twisted differential forms of this type have been used in quantum algebraic topology, and another example is given by the calculus of finite differences. The main result is the construction of a braiding \(R\) on \(\Omega^\bullet A\) such that \(R(a\otimes b)=b\otimes a\) and \(R(da\otimes b)=\alpha b\otimes da\) for \(a,b\in A\).