NSTL国家科技图书文献中心

1. On the quandles of isometries of the hyperbolic 3-space NSTL国家科技图书文献中心

Kai, Ryoya - 《Geometriae Dedicata》 - 2025,219(2) - 共14页

摘要：A quandle* is an algebraic structure whose* | conjugate quandle* of the orientation-preserving isometry* | quandle, denoted by Q(Gamma,gamma)documentclass[12pt | } is a non-trivial* element of Gammadocumentclass[12pt* | conjugate quandle* of PSL(2,C)documentclass[12pt]{minimal*

关键词： Quandle | Conjugate quandle | Homogeneous quandle | Hyperbolic Geometry | Kleinian group

2. CONSTRUCTIONS OF QUANDLES OVER GROUPS AND RINGS NSTL国家科技图书文献中心

Simonov, A. A. | Neshchadim, M. V.... - 《Siberian Mathematical Journal》 - 2024,65(3) - 627～638 - 共12页

摘要：: extension of a trivial* quandle by a group with a* | nontrivial abelian subgroup, a quandle* over a* | quandle presenting from a generalized Alexander quandle | antiautomorphism, and a quandle* over an n-dimensional module* | We present the following constructions

关键词： quandle | Hosszu quandle | trivial quandle | Alexander quandle | generalized Alexander quandle | self-distributivity | distributive | group | automorphism | antiautomorphism...

3. Quandle Rings, Idempotents and Cocycle Invariants of Knots NSTL国家科技图书文献中心

Swain, Dipali. - Mathematics.;Theoret... - Ph.D. - Elhamdadi, Mohamed - 2024, - 1～84 - 共84页

摘要： quandle of a non-trivial long knot exhibits non-trivial | quandles, a theory of quandle* rings analogous to the* | interconnections between quandles and their associated quandle | construction implies that morphisms of quandle* rings give a* | natural enhancement of the well-known quandle* coloring*

关键词： Idempotents | Knots | Quandle 2 cocycle | Quandle rings | Quandles

4. Quandle Theoretic Knot Invariants NSTL国家科技图书文献中心

Cazet, Nicholas. - Mathematics. - Ph.D. - Schultens, Jennifer - 2024, - 1～76 - 共76页

摘要： invariants. The axioms of a quandle* imply that the columns* | column. Their automorphism groups, quandle* polynomials* | - split surface-links of arbitrarily many trivial | study quandle* invariants of knotoids. The chapter* | quandle colorings and the shadow quandle cocycle

关键词： Knot invariant | Quandles | Surfaces in 4-manifold | Triple point numbers | Cocycle invariants

5. The State-Sum Invariants for Virtual Knot NSTL国家科技图书文献中心

Kazakov, A. A. - 《Lobachevskii journal of mathematics》 - 2023,44(12) - 5286～5293 - 共8页

摘要：We construct the new non-trivial* state-sum* | this work is based on cohomology quandle* theory and* | colorings of virtual knot and link diagrams by quandle | invariants for virtual knots and links by a generalization | of the powerful Carter-Saito-Jelsovsky-Kamada

关键词： virtual knots | virtual links | quandle | invariant state-sum | cohomology of quandle

6. Higher Coverings of Racks and Quandles-Part II SCIE Web of Science核心 NSTL国家科技图书文献中心

Renaud, Francois - 《Applied categorical structures》 - 2022,30(1) - 81～122 - 共42页 - 被引量：2

摘要： M. Eisermann's work on quandle* coverings, and the* | which are categorically central, relatively to trivial | induced Galois-theoretic concepts of trivial* covering* | This article is the second part of a series of | three articles, in which we develop a higher covering

关键词： Two-dimensional covering theory of racks and quandles | Categorical Galois theory | Double central extension | Commutator theory | Centralization | RELATIVE COMMUTATOR THEORY | GALOIS THEORY | ABSTRACT COMMUTATORS | CENTRAL EXTENSIONS | HOPF FORMULAS...

7. Abelian quandles and quandles with abelian structure group SCIE Web of Science核心 SCOPUS Scopus数据库 NSTL国家科技图书文献中心

Lebed, Victoria | Mortier, Arnaud - 《Journal of pure and applied algebra》 - 2021,225(1) - 共22页 - 被引量：2

摘要： structure group. The structure group of a finite quandle | of any abelian quandle* as a central extension of a* | group; and determine when the latter is trivial. In | structure group of any quandle* to its 2nd homology group H* | quandle with abelian structure group is torsion-free

关键词： Quandle | Structure group | Yang-Baxter equation | Rack homology

8. Quandles with orbit series conditions NSTL国家科技图书文献中心

Bonatto, M. | Crans, A.... - 《Journal of Algebra》 - 2021,567 - 284～309 - 共26页 - 被引量：2

摘要： a quandle. Using this notion we define four | trivial quandles while the classes OS and OSn correspond | We introduce the notion of an orbit series in | families of quandles based on finiteness conditions on | their orbit series. Intuitively, the classes tOS and

关键词： Quandle | Orbit series condition | Finite type condition | Engel group | Nilpotent group

9. ORDERABILITY OF LINK QUANDLES SCIE Web of Science核心 SCOPUS Scopus数据库 NSTL国家科技图书文献中心

HITESH RAUNDAL | MAHENDER SINGH ... - 《Proceedings of the Edinburgh Mathematical Society》 - 2021,64(2 Pt.3) - 620～649 - 共30页 - 被引量：2

摘要： quandles of most non-trivial* torus links are not right* | quandle of the trefoil is neither left nor right | certain non-trivial* positive (or negative) links are not* | The paper develops a general theory of | orderability of quandles with a focus on link quandles of

关键词： link quandle | link group | Montesinos link | orderable group | orderable quandle | torus link | quandle 2-cocycle

10. The lattice of subracks is atomic SCOPUS Scopus数据库 SCIE Web of Science核心 NSTL国家科技图书文献中心

Kiani, D. | Saki, A. - 《Journal of Combinatorial Theory, Series A》 - 2019,162 - 55～64 - 共10页 - 被引量：2

摘要： corresponding quandle* is the trivial *quandle. So the lattice | of a quandle. Moreover, we show that the lattice of | A rack is a set together with a self | -distributive bijective binary operation. In this paper, we | give a positive answer to a question due to

摘要：A quandle* is an algebraic structure whose* | conjugate quandle* of the orientation-preserving isometry* | quandle, denoted by Q(Gamma,gamma)documentclass[12pt | } is a non-trivial* element of Gammadocumentclass[12pt* | conjugate quandle* of PSL(2,C)documentclass[12pt]{minimal*

关键词： Quandle | Conjugate quandle | Homogeneous quandle | Hyperbolic Geometry | Kleinian group

摘要：: extension of a trivial* quandle by a group with a* | nontrivial abelian subgroup, a quandle* over a* | quandle presenting from a generalized Alexander quandle | antiautomorphism, and a quandle* over an n-dimensional module* | We present the following constructions

关键词： quandle | Hosszu quandle | trivial quandle | Alexander quandle | generalized Alexander quandle | self-distributivity | distributive | group | automorphism | antiautomorphism...

关键词： Idempotents | Knots | Quandle 2 cocycle | Quandle rings | Quandles

摘要： invariants. The axioms of a quandle* imply that the columns* | column. Their automorphism groups, quandle* polynomials* | - split surface-links of arbitrarily many trivial | study quandle* invariants of knotoids. The chapter* | quandle colorings and the shadow quandle cocycle

关键词： Knot invariant | Quandles | Surfaces in 4-manifold | Triple point numbers | Cocycle invariants

摘要：We construct the new non-trivial* state-sum* | this work is based on cohomology quandle* theory and* | colorings of virtual knot and link diagrams by quandle | invariants for virtual knots and links by a generalization | of the powerful Carter-Saito-Jelsovsky-Kamada

关键词： virtual knots | virtual links | quandle | invariant state-sum | cohomology of quandle

摘要： M. Eisermann's work on quandle* coverings, and the* | which are categorically central, relatively to trivial | induced Galois-theoretic concepts of trivial* covering* | This article is the second part of a series of | three articles, in which we develop a higher covering

关键词： Two-dimensional covering theory of racks and quandles | Categorical Galois theory | Double central extension | Commutator theory | Centralization | RELATIVE COMMUTATOR THEORY | GALOIS THEORY | ABSTRACT COMMUTATORS | CENTRAL EXTENSIONS | HOPF FORMULAS...

摘要： structure group. The structure group of a finite quandle | of any abelian quandle* as a central extension of a* | group; and determine when the latter is trivial. In | structure group of any quandle* to its 2nd homology group H* | quandle with abelian structure group is torsion-free

关键词： Quandle | Structure group | Yang-Baxter equation | Rack homology

摘要： a quandle. Using this notion we define four | trivial quandles while the classes OS and OSn correspond | We introduce the notion of an orbit series in | families of quandles based on finiteness conditions on | their orbit series. Intuitively, the classes tOS and

关键词： Quandle | Orbit series condition | Finite type condition | Engel group | Nilpotent group

摘要： quandles of most non-trivial* torus links are not right* | quandle of the trefoil is neither left nor right | certain non-trivial* positive (or negative) links are not* | The paper develops a general theory of | orderability of quandles with a focus on link quandles of

关键词： link quandle | link group | Montesinos link | orderable group | orderable quandle | torus link | quandle 2-cocycle

摘要： corresponding quandle* is the trivial *quandle. So the lattice | of a quandle. Moreover, we show that the lattice of | A rack is a set together with a self | -distributive bijective binary operation. In this paper, we | give a positive answer to a question due to

关键词： Rack | Quandle | Lattice of subracks | Atomic lattice | Distributive lattice

4008-161-200 800-990-8900

国家科技图书文献中心

摘要：A quandle is an algebraic structure whose | conjugate quandle of the orientation-preserving isometry | quandle, denoted by Q(Gamma,gamma)documentclass[12pt | } is a non-trivial element of Gammadocumentclass[12pt | conjugate quandle of PSL(2,C)documentclass[12pt]{minimal

关键词： Quandle | Conjugate quandle | Homogeneous quandle | Hyperbolic Geometry | Kleinian group

摘要：: extension of a trivial quandle by a group with a | nontrivial abelian subgroup, a quandle over a | quandle presenting from a generalized Alexander quandle | antiautomorphism, and a quandle over an n-dimensional module | We present the following constructions

关键词： quandle | Hosszu quandle | trivial quandle | Alexander quandle | generalized Alexander quandle | self-distributivity | distributive | group | automorphism | antiautomorphism...

关键词： Idempotents | Knots | Quandle 2 cocycle | Quandle rings | Quandles

摘要： invariants. The axioms of a quandle imply that the columns | column. Their automorphism groups, quandle polynomials | - split surface-links of arbitrarily many trivial | study quandle invariants of knotoids. The chapter | quandle colorings and the shadow quandle cocycle

关键词： Knot invariant | Quandles | Surfaces in 4-manifold | Triple point numbers | Cocycle invariants

摘要：We construct the new non-trivial state-sum | this work is based on cohomology quandle theory and | colorings of virtual knot and link diagrams by quandle | invariants for virtual knots and links by a generalization | of the powerful Carter-Saito-Jelsovsky-Kamada

关键词： virtual knots | virtual links | quandle | invariant state-sum | cohomology of quandle

摘要： M. Eisermann's work on quandle coverings, and the | which are categorically central, relatively to trivial | induced Galois-theoretic concepts of trivial covering | This article is the second part of a series of | three articles, in which we develop a higher covering

关键词： Two-dimensional covering theory of racks and quandles | Categorical Galois theory | Double central extension | Commutator theory | Centralization | RELATIVE COMMUTATOR THEORY | GALOIS THEORY | ABSTRACT COMMUTATORS | CENTRAL EXTENSIONS | HOPF FORMULAS...

摘要： structure group. The structure group of a finite quandle | of any abelian quandle as a central extension of a | group; and determine when the latter is trivial. In | structure group of any quandle to its 2nd homology group H | quandle with abelian structure group is torsion-free

关键词： Quandle | Structure group | Yang-Baxter equation | Rack homology

摘要： a quandle. Using this notion we define four | trivial quandles while the classes OS and OSn correspond | We introduce the notion of an orbit series in | families of quandles based on finiteness conditions on | their orbit series. Intuitively, the classes tOS and

关键词： Quandle | Orbit series condition | Finite type condition | Engel group | Nilpotent group

摘要： quandles of most non-trivial torus links are not right | quandle of the trefoil is neither left nor right | certain non-trivial positive (or negative) links are not | The paper develops a general theory of | orderability of quandles with a focus on link quandles of

关键词： link quandle | link group | Montesinos link | orderable group | orderable quandle | torus link | quandle 2-cocycle

摘要： corresponding quandle is the trivial quandle. So the lattice | of a quandle. Moreover, we show that the lattice of | A rack is a set together with a self | -distributive bijective binary operation. In this paper, we | give a positive answer to a question due to

关键词： Rack | Quandle | Lattice of subracks | Atomic lattice | Distributive lattice

4008-161-200 800-990-8900

国家科技图书文献中心

摘要：A quandle* is an algebraic structure whose* | conjugate quandle* of the orientation-preserving isometry* | quandle, denoted by Q(Gamma,gamma)documentclass[12pt | } is a non-trivial* element of Gammadocumentclass[12pt* | conjugate quandle* of PSL(2,C)documentclass[12pt]{minimal*

摘要：: extension of a trivial* quandle by a group with a* | nontrivial abelian subgroup, a quandle* over a* | quandle presenting from a generalized Alexander quandle | antiautomorphism, and a quandle* over an n-dimensional module* | We present the following constructions

摘要： invariants. The axioms of a quandle* imply that the columns* | column. Their automorphism groups, quandle* polynomials* | - split surface-links of arbitrarily many trivial | study quandle* invariants of knotoids. The chapter* | quandle colorings and the shadow quandle cocycle

摘要：We construct the new non-trivial* state-sum* | this work is based on cohomology quandle* theory and* | colorings of virtual knot and link diagrams by quandle | invariants for virtual knots and links by a generalization | of the powerful Carter-Saito-Jelsovsky-Kamada

摘要： M. Eisermann's work on quandle* coverings, and the* | which are categorically central, relatively to trivial | induced Galois-theoretic concepts of trivial* covering* | This article is the second part of a series of | three articles, in which we develop a higher covering

摘要： structure group. The structure group of a finite quandle | of any abelian quandle* as a central extension of a* | group; and determine when the latter is trivial. In | structure group of any quandle* to its 2nd homology group H* | quandle with abelian structure group is torsion-free

摘要： quandles of most non-trivial* torus links are not right* | quandle of the trefoil is neither left nor right | certain non-trivial* positive (or negative) links are not* | The paper develops a general theory of | orderability of quandles with a focus on link quandles of

摘要： corresponding quandle* is the trivial *quandle. So the lattice | of a quandle. Moreover, we show that the lattice of | A rack is a set together with a self | -distributive bijective binary operation. In this paper, we | give a positive answer to a question due to