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4 results on '"57M25, 53C30"'

1. On classification of quandles of cyclic type

Author

Kamada, Seiichi, Tamaru, Hiroshi, and Wada, Koshiro

Subjects
Mathematics - Geometric Topology, Mathematics - Differential Geometry, 57M25, 53C30
Abstract

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic type with cardinality up to $12$., Comment: 14 pages

Published
2013

2. Two-point homogeneous quandles with prime cardinality

Author

Tamaru, Hiroshi

Subjects
Mathematics - Geometric Topology, Mathematics - Differential Geometry, 57M25, 53C30
Abstract

Quandles can be regarded as generalizations of symmetric spaces. Among symmetric spaces, two-point homogeneous Riemannian manifolds would be the most fundamental ones. In this paper, we define two-point homogeneous quandles analogously, and classify those with prime cardinality., Comment: 15 pages

Published
2013
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3. On classification of quandles of cyclic type

Author

Hiroshi Tamaru, Koshiro Wada, and Seiichi Kamada

Subjects
Mathematics - Differential Geometry, General Mathematics, 010102 general mathematics, Geometric Topology (math.GT), Type (model theory), 01 natural sciences, Mathematics::Algebraic Topology, Mathematics::Geometric Topology, Subclass, 53C35, Combinatorics, Set (abstract data type), Mathematics - Geometric Topology, Cardinality, Differential Geometry (math.DG), Mathematics::K-Theory and Homology, Mathematics::Quantum Algebra, 57M25, 0103 physical sciences, 57M25, 53C30, FOS: Mathematics, 010307 mathematical physics, Isomorphism, 0101 mathematics, Mathematics
Abstract

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic type with cardinality up to $12$., 14 pages

Published
2013

4. Two-point homogeneous quandles with prime cardinality

Author

Hiroshi Tamaru

Subjects
Mathematics - Differential Geometry, quandles, General Mathematics, symmetric spaces, 53C30, Geometric Topology (math.GT), Mathematics::Geometric Topology, Prime (order theory), two-point homogeneous Riemannian manifolds, Combinatorics, Mathematics - Geometric Topology, Differential Geometry (math.DG), Homogeneous, 57M25, 57M25, 53C30, FOS: Mathematics, Cardinality (SQL statements), Point (geometry), Mathematics
Abstract

Quandles can be regarded as generalizations of symmetric spaces. Among symmetric spaces, two-point homogeneous Riemannian manifolds would be the most fundamental ones. In this paper, we define two-point homogeneous quandles analogously, and classify those with prime cardinality., Comment: 15 pages

Published
2013

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