Quandle rings

DOI10.1142/S0219498819501573zbMath1473.17087arXiv1709.03069OpenAlexW2798384146MaRDI QIDQ5230124

Mahender Singh, Inder Bir Singh Passi, Valeriy G. Bardakov

Publication date: 20 August 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.03069

zbMATH Keywords

unit groupknot quandleconnected quandlepower associativityquandle ringquotient quandleLatin quandlerack ring

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Group rings (16S34) Sets with a single binary operation (groupoids) (20N02) Other nonassociative rings and algebras (17D99) Generalized knots (virtual knots, welded knots, quandles, etc.) (57K12)

Related Items

Idempotents, free products and quandle coverings ⋮ Zero-divisors and idempotents in quandle rings ⋮ QUANDLE G-ALGEBRA OVER A FIELD ⋮ Derivation problem for quandle algebras ⋮ Enhancements of link colorings via idempotents of quandle rings ⋮ Knot groups, quandle extensions and orderability ⋮ Ring theoretic aspects of quandles ⋮ Embeddings of quandles into groups ⋮ Quandle rings ⋮ Nontrivial topological quandles

Cites Work

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• Automorphism groups of Alexander quandles.
• Cohomology of categorical self-distributivity
• Connected quandles and transitive groups
• A classifying invariant of knots, the knot quandle
• Group rings and their augmentation ideals
• From racks to pointed Hopf algebras
• Automorphism groups of quandles arising from groups
• Ring theoretic aspects of quandles
• Trunks and classifying spaces
• Automorphism groups of quandles and related groups
• Cohomology of the adjoint of Hopf algebras.
• Spiegelungsräume und homogene symmetrische Räume
• Extensions of racks and quandles
• Yang-Baxter deformations of quandles and racks
• Matrices and finite quandles
• Flat connected finite quandles
• On quandle homology groups of Alexander quandles of prime order
• A Survey of Quandle Ideas
• Classification of flat connected quandles
• TOWARD A CLASSIFICATION OF FINITE QUANDLES
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• James bundles
• Quandle rings
• AUTOMORPHISM GROUPS OF QUANDLES
• Reflexion spaces and homogeneous symmetric spaces