Linear extensions of multiple conjugation quandles and MCQ Alexander pairs
نویسندگان
چکیده
منابع مشابه
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 known distinct connected finite Alexander quandles.
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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. ...
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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.
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Cocycles are constructed by polynomial expressions for Alexander quandles. As applications, non-triviality of some quandle homology groups are proved, and quandle cocycle invariants of knots are studied. In particular, for an infinite family of quandles, the non-triviality of quandle homology groups is proved for all odd dimensions.
متن کاملExtensions of Racks and Quandles
A rack is a set equipped with a bijective, self-right-distributive binary operation, and a quandle is a rack which satisfies an idempotency condition. In this paper, we introduce a new definition of modules over a rack or quandle, and show that this definition includes the one studied by Etingof and Graña [9] and the more general one given by Andruskiewitsch and Graña [1]. We further show that ...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2020
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498821500456