Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Truman, Paul J."'
Skew braces provide an algebraic framework for studying bijective nondegenerate solutions of the set-theoretic Yang-Baxter equation. We show that left skew bracoids, recently introduced by two of the authors, can be used to obtain right nondegenerate
Externí odkaz:
http://arxiv.org/abs/2404.15929
Autor:
Martin-Lyons, Isabel, Truman, Paul J.
Skew braces are intensively studied owing to their wide ranging connections and applications. We generalize the definition of a skew brace to give a new algebraic object, which we term a skew bracoid. Our construction involves two groups interacting
Externí odkaz:
http://arxiv.org/abs/2305.15848
Autor:
Truman, Paul J.
The Hopf-Galois structures admitted by a Galois extension of fields $ L/K $ with Galois group $ G $ correspond bijectively with certain subgroups of $ \mathrm{Perm}(G) $. We use a natural partition of the set of such subgroups to obtain a method for
Externí odkaz:
http://arxiv.org/abs/2208.12054
Autor:
Martin-Lyons, Isabel, Truman, Paul J.
Publikováno v:
In Journal of Algebra 15 January 2024 638:751-787
We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an endomorphism gives rise to two non-degenerate solutions to the Yang-B
Externí odkaz:
http://arxiv.org/abs/2006.13196
Autor:
Koch, Alan, Truman, Paul J.
Given a finite group $ G $, we study certain regular subgroups of the group of permutations of $ G $, which occur in the classification theories of two types of algebraic objects: skew left braces with multiplicative group isomorphic to $ G $ and Hop
Externí odkaz:
http://arxiv.org/abs/2005.05809
Autor:
Koch, Alan, Truman, Paul J.
Given a skew left brace $\mathfrak{B}$, we introduce the notion of an "opposite" skew left brace $\mathfrak{B}'$, which is closely related to the concept of the opposite of a group, and provide several applications. Skew left braces are closely linke
Externí odkaz:
http://arxiv.org/abs/1908.02682
Autor:
Truman, Paul J
Let $ K $ be a number field and let $ L/K $ be a tamely ramified radical extension of prime degree $ p $. If $ K $ contains a primitive $ p^{th} $ root of unity then $ L/K $ is a cyclic Kummer extension; in this case the group algebra $ K[G] $ (with
Externí odkaz:
http://arxiv.org/abs/1812.09394
Autor:
Taylor, Stuart, Truman, Paul J
Let $L/F$ be a Galois extension of fields with Galois group isomorphic to the quaternion group of order $ 8 $. We describe all of the Hopf-Galois structures admitted by $ L/F $, and determine which of the Hopf algebras that appear are isomorphic as H
Externí odkaz:
http://arxiv.org/abs/1809.09497
Let $ L/K $ be a finite separable extension of fields whose Galois closure $ E/K $ has group $ G $. Greither and Pareigis have used Galois descent to show that a Hopf algebra giving a Hopf-Galois structure on $ L/K $ has the form $ E[N]^{G} $ for som
Externí odkaz:
http://arxiv.org/abs/1711.05554