9 citations · 24 across the 12 of their papers we have counts for
11 papers · 1 filter
Set-theoretic solutions of the Yang--Baxter equation, associated quadratic algebras and the minimality condition
F. Cedo, E. Jespers, J. Okninski
Given a finite non-degenerate set-theoretic solution of the Yang-Baxter equation and a field , the structure -algebra of is $A=A(K,X,r)=K\langle X\mid xy=uv \…
Gröbner basis and the automaton property of Hecke--Kiselman algebras
Arkadiusz Mȩcel, Jan Okniński
It is shown that the Hecke-Kiselman algebra associated to a finite directed graph is an automaton algebra in the sense of Ufnarovskii. Consequently, its Gelfand-Kirillov dimension…
Braces and the Yang-Baxter equation
Ferran Cedo, Eric Jespers, Jan Okninski
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In pa…
Grobner-Shirshov bases for plactic algebras
Lukasz Kubat, Jan Okninski
A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobn…
Structure of Chinese algebras
Joanna Jaszunska, Jan Okninski
The structure of the algebra K[M] of the Chinese monoid M over a field K is studied. The minimal prime ideals are described. They are determined by certain homogeneous congruences…
Algebras and groups defined by permutation relations of alternating type
Ferran Cedo, Eric Jespers, Jan Okninski
The class of finitely presented algebras over a field with a set of generators and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{σ(1)…
Finitely presented algebras and groups defined by permutation relations
F. Cedo, E. Jespers, J. Okninksi
The class of finitely presented algebras over a field with a set of generators and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{σ(a)…
Semigroup algebras of submonoids of polycyclic-by-finite groups and maximal orders
Isabel Goffa, Eric Jespers, Jan Okninski
Necessary and sufficient conditions are given for a prime Noetherian algebra K[S] of a submonoid S of a polycyclic-by-finite group G to be a maximal order. These conditions are ent…
Normal domains with monomial presentations
Isabel Goffa, Eric Jespers, Jan Okninski
Let A be a finitely generated commutative algebra over a field K with a presentation A=K < X_{1}, ..., X_{n} | R >, where R is a set of monomial relations in the generators X_{1},…
Primes of height one and a class of Noetherian finitely presented algebras
Isabel Goffa, Eric Jespers, Jan Okninski
Constructions are given of Noetherian maximal orders that are finitely presented algebras over a field K, defined by monomial relations. In order to do this, it is shown that the u…
Quadratic algebras of skew type and the underlying semigroups
T. Gateva-Ivanova, Eric Jespers, Jan Okninski
We consider algebras over a field K defined by a presentation K <x_1,..., x_n : R >, where consists of n choose 2 square-free relations of the form x_i x_j = x_k x_l with every…