Bijective 1-cocycles, braces, and non-commutative prime factorization
From MaRDI portal
Publication:5867735
DOI10.4064/cm8684-2-2022OpenAlexW4285116742WikidataQ114022001 ScholiaQ114022001MaRDI QIDQ5867735
Publication date: 14 September 2022
Published in: Colloquium Mathematicum (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4064/cm8684-2-2022
hereditary orderbraceprime factorizationright \(\ell\)-groupnon-commutative curvedivisor groupbijective cocyclequasi-Garside group
Noncommutative algebraic geometry (14A22) Braid groups; Artin groups (20F36) Ordered semigroups and monoids (06F05) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60) Representation of semigroups; actions of semigroups on sets (20M30) Yang-Baxter equations (16T25) Group actions on combinatorial structures (05E18) Relations with noncommutative geometry (11M55)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation.
- Cohomology and extensions of braces
- Hereditary arithmetics
- Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
- Weighted noncommutative regular projective curves
- Multipermutation solutions of the Yang-Baxter equation
- Right-ordered groups
- Monoids and groups of I-type.
- Braces, radical rings, and the quatum Yang-Baxter equation.
- The Kazhdan-Lusztig cells in certain affine Weyl groups
- Classical solutions of the quantum Yang-Baxter equation
- Groupes et anneaux reticules
- Semigroups of \(I\)-type
- Orderings of mapping class groups after Thurston
- On the set-theoretical Yang-Baxter equation
- Order automatic mapping class groups
- Artin groups of Euclidean type
- Orderable 3-manifold groups.
- A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
- Transitive subgroups of primitive permutation groups
- Homological properties of Sklyanin algebras
- Set-theoretical solutions to the quantum Yang-Baxter equation
- Classification of the affine structures of a generalized quaternion group of order \(\geqslant 32\)
- Dual Euclidean Artin groups and the failure of the lattice property.
- Foundations of Garside theory
- Decomposition of Garside groups and self-similar \(L\)-algebras
- Braces and the Yang-Baxter equation
- Hereditary noetherian categories of positive Euler characteristic
- Right \(l\)-groups, geometric Garside groups, and solutions of the quantum Yang-Baxter equation
- Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs.
- Hereditary Noetherian prime rings
- Les immeubles des groupes de tresses généralises
- Artin-Gruppen und Coxeter-Gruppen
- Lattice-ordered groups
- Noetherian hereditary abelian categories satisfying Serre duality
- Abelian Hopf Galois structures on prime-power Galois field extensions
- Hopf braces and Yang-Baxter operators
- Skew braces and the Yang–Baxter equation
- Some Examples of Square Integrable Representations of Semisimple p-Adic Groups
- Garside Groups and Yang–Baxter Equation
- Groupes de Garside
- Generalized radical rings, unknotted biquandles, and quantum groups
- Involutive Yang-Baxter groups
- REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS
- Constructions of Hereditary Noetherian Rings and Simple Rings
- On some unsolved problems in quantum group theory
- Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
- On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation
- Left Braces and the Quantum Yang–Baxter Equation
- Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
- Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles
- A GEOMETRIC AND ALGEBRAIC DESCRIPTION OF ANNULAR BRAID GROUPS
- Fixed-point free endomorphisms and Hopf Galois structures
- ON REGULAR SUBGROUPS OF THE AFFINE GROUP
- Classification of cyclic braces, II
- Set-theoretic solutions to the Yang–Baxter equation, skew-braces, and related near-rings
- THE BRAID GROUP AND OTHER GROUPS
- Two Remarks About Hereditary Orders
- Hereditary Orders
- Structure of hereditary orders
- Counterexample to a conjecture about braces.
