Schur multipliers and second quandle homology. (English) Zbl 1439.57027
Summary: We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its structure and provide some computational examples.
MSC:
| 57K12 | Generalized knots (virtual knots, welded knots, quandles, etc.) |
| 19C09 | Central extensions and Schur multipliers |
| 20J06 | Cohomology of groups |
| 20J05 | Homological methods in group theory |
Keywords:
quandle; group homology; rack and quandle homology; Schur multiplier; exterior algebra; central extensions; semi-Hopfian groupReferences:
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