Browsing by Author "Vendramin, Leandro"

Now showing 1 - 5 of 5
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    Computer Algebra with GAP
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2023) Piterman, Kevin I.; Vendramin, Leandro
    This monograph includes the following topics: a basic introduction to the language, basic arithmetic, permutations, matrices, polynomial rings, finite fields, finite and finitely presented groups, small groups, group representations and character theory, and simple groups. Advanced topics include testing several open conjectures and theorems. In addition, each chapter ends with an extensive list of problems. We hope the reader will find some problems challenging and exciting as they are based on outstanding research papers. Selected solutions can be found at the end of the book.
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    Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation
    (Zürich : EMS Publ. House, 2019) Lebed, Victoria; Rump, Wolfgang; Vendramin, Leandro
    The workshop was focused on three facets of the interplay between set-theoretic solutions to the Yang--Baxter equation and classical algebraic structures (groups, monoids, algebras, lattices, racks etc.): structures used to construct new solutions; structures as invariants of solutions; and YBE as a source of structures with interesting properties.
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    Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations
    (Zürich : EMS Publ. House, 2024) Carnovale, Giovanna; Heckenberger, István; Vendramin, Leandro
    Nichols algebras are graded Hopf algebra objects in braided tensor categories. They appeared first in a paper by Nichols in 1978 in the search for new examples of Hopf algebras. Rediscovered later several times, they also provide a conceptual explanation of the construction of quantum groups. The aim of the workshop is to review recent developments in the field, initiate collaborations, and discuss new approaches to open problems.
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    On the Enumeration of Finite L-Algebras
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2022) Dietzel, Carsten; Menchón, Paula; Vendramin, Leandro
    We use Constraint Satisfaction Methods to construct and enumerate finite L-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang-Baxter equation. There are 377322225 isomorphism classes of L-algebras of size eight. The database constructed suggest the existence of bijections between certain classes of L-algebras and well-known combinatorial objects. On the one hand, we prove that Bell numbers enumerate isomorphism classes of finite linear L-algebras. On the other hand, we also prove that finite regular L-algebras are in bijective correspondence with infinite-dimensional Young diagrams.
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    Skew Braces and the Yang-Baxter Equation
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2023) Brzeziński, Tomasz; Colazzo, Ilaria; Doikou, Anastasia; Vendramin, Leandro
    The workshop was focused on the interplay between set-theoretic solutions to the Yang-Baxter equation and several algebraic structures used to construct and understand new solutions. In this vein, the YBE and properties of these algebraic structures are used as a source of inspiration to study other mathematical problems not directly related to the YBE.