The Anick resolution (Q1196802): Difference between revisions

\textit{D. J. Anick} [Trans. Am. Math. Soc. 269, 641-659 (1986; Zbl 0598.16028)] constructs a free resolution of a field \(k\) over any algebra presented by the free algebra \(k\{X_ 1,\dots,X_ n\}\) with relations in the augmentation ideal. The author shows that the maps in that resolution have an explicit decomposition using the tools of noncommutative Gröbner bases theory [\textit{F. Mora}, Proc. 3rd Int. Conf., Grenoble/France 1985, Lect. Notes Comput. Sci. 229, 353-363 (1986; Zbl 0659.16003)]. An evidence of that has been found by \textit{E. L. Green} et al. [Commun. Algebra 21, No. 6, 1869-1887 (1993; Zbl 0796.16006)].