An explicit description of the second cohomology group of a quandle

Abstract

We use the inflation-restriction sequence and a result of Etingof and Graña on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles with values in an abelian group. Several applications are given.

22 pages. Accepted for publication in Mathematische Zeitschrift

References in corpus (3)

• Nichols algebras of group type with many quadratic relations
• Quandle Colorings of Knots and Applications
• Two-point homogeneous quandles with prime cardinality

Cited by in corpus (4)

• Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
• Abelian quandles and quandles with abelian structure group
• Quandle cohomology, extensions and automorphisms
• Schur Multipliers and Second Quandle Homology