Matrices and finite Alexander quandles
نویسندگان
چکیده
We describe an algorithm for determining whether a finite quandle is isomorphic to an Alexander quandle by finding all possible Alexander presentations of the quandle. We give an implementation of this algorithm in Maple.
منابع مشابه
Classification of Finite Alexander Quandles
Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1 − t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t − a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. ...
متن کاملTopology Proceedings CLASSIFICATION OF FINITE ALEXANDER QUANDLES
Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1− t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t− a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. We...
متن کاملSe p 20 06 Alexander quandles of order 16
Isomorphism classes of Alexander quandles of order 16 are determined, and classes of connected quandles are identified. This paper extends the list of distinct connected finite Alexander quandles.
متن کاملAlexander Quandles of Order 16 *
Isomorphism classes of Alexander quandles of order 16 are determined, and classes of connected quandles are identified. This paper extends the list of known distinct connected finite Alexander quandles.
متن کاملThe 3-cocycles of the Alexander quandles Fq[T]/(T − ω)
We determine the third cohomology group of the Alexander quandles of the form Fq[T ]/(T − ω). Here Fq denotes the finite field of order q, and ω denotes an element of Fq which is neither 0 nor 1. As a result, we obtain many concrete examples of non-trivial 3-cocycles.
متن کامل