Noncommutative and non-associative structures, braces and applications | ||

Monday, March 12 | ||

09:15-09:45 | Vladimir Bavula | TBA |

09:55-10:25 | Eric Jespers (Vrije U, Brussel) | Groups, Rings, Braces and Set-theoretic Solutions of the Yang-Baxter Equation (abstract) |

10:35-11:05 | Jan Okniński | Hecke-Kiselman algebras: combinatorics and structure (abstract) |

11:25-11:55 | Michal Ziembowski (Warsaw U Tech, Poland) | Lie solvability in matrix algebras (abstract) |

12:05-12:35 | Alexei Belov (Bar Ilan U, Israel) | Automorphisms of Weyl Algebra and a Conjecture of Kontsevich (abstract) |

12:35-14:00 | Lunch | |

14:00-14:15 | Marco Castelli (U Salento, Italy) | Indecomposable left cycle sets (abstract) |

14:20-14:35 | Giuseppina Pinto (U Salento, Italy) | Indecomposable simple left cycle sets (abstract) |

14:40-15:10 | Michael Wemyss | Contraction Algebras and their Properties (abstract) |

15:20-15:50 | Tatiana Gateva-Ivanova (Amer U Bulgraria) | TBA |

16:00-16:30 | Be'eri Greenfeld (Bar Ilan U, Israel) | Growth, relations and prime spectra of monomial algebras (abstract) |

Tuesday, March 13 | ||

09:00-09:30 | Agata Pilitowska (Warsaw U of Tech, Poland) | Medial solutions to QYBE - 1 (abstract) |

09:40-10:10 | Anna Zamojska (Warsaw U of Tech, Poland) | Medial solutions to QYBE - 2 (abstract) |

10:20-10:50 | Fabienne Chouraqui (Oranim, Haifa, Israel) | Finite quotients of quantum Yang-Baxter groups (abstract) |

11:10-11:40 | Andre Leroy (U d'Artois, Lens, France) | Multivariate polynomial maps and pseudo linear transformations (abstract) |

11:50-12:20 | Christian Lomp (U Porto, Portugal) | Finiteness conditions on the injective hull of simple modules. (abstract) |

12:30-13:00 | Tomasz Brzezinski (Swansea U, UK) | Trusses (abstract) |

Wednesday, March 14 | ||

09:30-10:00 | Florin Nichita (Inst Mat Romanian Acad) | Non-associative structures, QYBE and applications (abstract) |

10:10-10:40 | Francesco Catino (U of Salento, Italy) | Set-theoretic solutions of the pentagon equation (abstract) |

10:50-11:20 | Ferran Cedó (U Autonoma de Barcelona, Spain) | Garside structures on the structure group of finite solutions of the Yang-Baxter equation. (abstract) |

11:40-12:10 | Wolfgang Rump (U Stuttgart, Germany) | Skew-braces and near-rings meeting in Malta (abstract) |

12:20-12:50 | Susan Sierra | TBA |

12:50-14:15 | Lunch | |

14:15-14:30 | Ilaria Colazzo | The matched product of the solutions of the Yang-Baxter equation (abstract) |

14:40-14:55 | Paola Stefanelli | The matched product of semi-braces (abstract) |

15:05-15:20 | Arne Van Antwerpen | Left semi-braces and solutions to the Yang-Baxter equation (abstract) |

15:25-15:40 | Kayvan Nejabati Zenouz (Univeristy of Exeter, UK) | Hopf-Galois structures and skew braces (abstract) |

15:50-16:20 | Jerzy Matczuk (Warsaw University) | On Some Questions Related to Köthe's Problem (abstract) |

Thursday, March 15 | ||

09:00-09:30 | Ivan Shestakov (U Sao Paulo, Brazil) | Speciality problem for Malcev algebras. (abstract) |

09:40-09:55 | Agata Smoktunowicz (U Edinburgh) | On interactions between noncommutative rings, braces and geometry (abstract) |

10:00-10:15 | Natalja Iyudu | TBA |

10:20-10:35 | Petr Vojtechovsky (U Denver) | Simply connected latin quandles (abstract) |

10:45-11:15 | David Stanovsky | |

11:25-11:55 | Bernhard Amberg (U Mainz, Germany) | TBA |

By order of appearance

In order to describe all set-theoretic non-degenerate (i.e. each σ

We will also consider two related questions, namely whether, for a field F, an Ls

In the talk, the plan of attack on Kontsevich conjecture called lifting of symplectomorphisms is presented. Starting with a polynomial symplectomorphism, one can lift it to an automorphism of the power series completion of the Weyl algebra (with commutation relations preserved), after which one can successfully eliminate the relevant terms in the power series (given by the images of Weyl algebra generators under the lifted automorphism) to make them into polynomials. Thus one obtains a candidate for the Kontsevich isomorphism.

The procedure utilizes the following essential features. First, the Weyl algebra over an algebraically closed field of characteristic zero may be identified with a subalgebra in a certain reduced direct product (reduction modulo infinite prime) of Weyl algebras in positive characteristic - a fact that allows one to use the theory of Azumaya algebras and is particularly helpful when eliminating the infinite series. Second, the lifting is performed via a direct homomorphism Aut(W

(This is joint work with A. Elishev and J.-T. Yu)

In this talk we provide a characterization of a large family of indecomposable finite left cycle sets written in terms of dynamical extensions [2,4].

We apply this to construct affine monomial algebras growing arbitrarily close to quadraticly, having arbitrarily long chains of prime ideals; this answers a question of Bergman. Previous known counterexamples to Bergman's question, due to Bell, are not constructive so there is much less control on their growth and structure; in particular, our examples are the first graded counterexamples to Bergman's question. On the other hand, graded algebras of quadratic growth have bounded chains of primes, thus our result is close to optimal.

As another application of our construction, we are able to show that monomial algebras defined by sparse enough subexponentially (resp. polynomially) many relations of each degree can be mapped onto prime monomial algebras of intermediate growth (resp. finite GK-dimension). This provides a strengthened analogy for the case of monomial algebras of Smoktunowicz's answer to questions of Zelmanov and Drensky in the case of sparsely related Golod-Shafarevich algebras.

This is a joint work with P. Jedlička and D. Stanovský [2, 3]. A binary algebra (Q,*) is called a

As a consequence of the axioms (1)-(2), each left translation L

A quandle Q is called

This is a joint work with Eddy Godelle - Universite de Caen, France

While the first Weyl algebra A

In this talk I will shortly report on classes of non-commutative Noetherian rings, like enveloping algebras of Lie algebras and some Ore extensions over commutative rings, that satisfy a weak form of Matlis' theorem. Instead of dropping commutativity one might drop also the Noetherian condition in Matlis' theorem and I will finish my talk with some results on commutative, non-Noetherian rings that satisfy a weak form of Matlis' theorem. The later results were obtained jointly with P. Carvalho and P. Smith.

These solutions appear for the first time in S. Zakrzewski,

In the talk I will present the old and the new results about this type of solutions and I will select some open problems.

We show that nevertheless, every skew-brace A is a complete invariant of a near ring, the initial object of a category of near-rings associated to A. The terminal object is the above mentioned near-ring of self-maps. Moreover, it will be shown that near-rings and skew-braces admit a common specialization as well as a common generalization: They live on the same island (the same category) and give birth to a structure that is a near-ring and skew-brace at the same time. Birds of a feather flock together.

One of these problems is how to construct new families of solutions. Initial contribution to this aspect has been given by Etingof, Schedler, and Soloviev, who present a method to obtain a new solution via retraction. Recently, Vendramin in [9] and Bachiller, Cedó, Jespers, Okniński in [1] provide methods to obtain families of solutions starting from others, which are known.

In this talk we introduce a novel construction technique, called

In this talk we focus on a new construction of semi-braces, the

Bibliography: [1] P. Kanwar, A. Leroy & J. Matczuk,

If A is an alternative algebra then it forms a Malcev algebra A

The problem of speciality, formulated by A.I.Malcev in 1955, asks whether any Malcev algebra is isomorphic to a subalgebra of A