The next meeting of the Algebra and Logic Seminar will be held online via Zoom on March 22, 2024 (Friday) at 1:00 pm (UTC+2). A talk on: On the uniqueness of maximal solvable extensions of nilpotent Lie algebras will be delivered by Bakhrom A. Omirov (Harbin Institute of Technologies, Harbin, China and Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Uzbekistan). Abstract.During the talk it will be shown that under certain condition an arbitrary complex finite-dimensional maximal extension of a nilpotent Lie algebra N is isomorphic to the semidirect sum of N and its maximal torus. A criterion of the completeness for a finite-dimensional solvable Lie algebra is established. Comparisons with some existing results will also be discussed. Link to the Zoom room: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09   Algebra and Logic [...]

The next meeting of the Algebra and Logic Seminar will be held online via Zoom on February 23, 2024 (Friday) at 1:00 pm (UTC+2). A talk on: Invariant subalgebras of the rational Cherednik algebra will be delivered by Niall Hird (University of Glasgow, UK). Abstract. The rational Cherednik algebra is a degeneration of the double affine Hecke algebra and an object of interest to many representation theorists, it also has strong connections to integrable systems. In my talk I will discuss two subalgebras that arise from considering the invariants of the action of reductive subgroups of the special linear group. In particular we will examine the centres of these invariant subalgebras and compare with the algebra of invariants of the centre of the entire [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrid format in Room 578 of IMI - BAS and online via Zoom on January 8, 2024 (Monday) at 1:00 pm (UTC+2). A talk on: On the exceptional series and its siblings will be delivered by Bruce Westbury (retired from University of Warwick, UK). Abstract. The exceptional series is the following series of eight simple Lie algebras: A1, A2, G2, D4, F4, E6, E7, E8 Consider each Lie algebra, g, as a representation of the group Aut(g). Then the centraliser algebras of the first five tensor powers of g have common structure. First, they have the same branching rules. We introduce a parameter so that the exceptional series is a set [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrod format (in Room 578 of IMI - BAS and online via Zoom) on December 1, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: Characterization of Ideals of Q-algebras Related to its G-part will be delivered by Jörg Koppitz (IMI - BAS, Bulgaria). Abstract. In this presentation, we study the G -part of Q -algebras X , i.e. the set G(X)=\{x\in X:0x=x\} . We show that G(X) is an abelian group, whenever G(X) is an ideal and characterize all Q -algebras X such that G(X) is an ideal of X . Moreover, we show that, up to isomorphism, there is only one Q -algebra X with G(X)=X , [...]

The next meeting of the Algebra and Logic Seminar will be held online on November 24, 2023 (Friday) at 1:00 pm (UTC+2) with two talks. At 1:00 pm (UTC+2) Dimitrinka Vladeva (IMI - BAS) will deliver a talk on Catalan numbers and additively idempotent semirings At 2:00 pm (UTC+2) Roussanka Loukanova (IMI - BAS) will deliver a talk on Semantics of Propositional Attitudes in Type-Theory of Algorithms Title: Catalan numbers and additively idempotent semirings Abstract. The purpose of the present talk is to provide new applications of remarkable Catalan numbers. In Richard Stanley’s book Enumerative Combinatorics, Volume II (Cambridge University Press) there are many combinatorial objects that are counted by the Catalan numbers as well as applications in graph theory, Young diagrams, lattice theory, real matrices, [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrod format (in Room 578 of IMI - BAS and online via Zoom) on November 17, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: Noncommutative invariants of dihedral groups will be delivered by Boyan Kostadinov (IMI - BAS, Bulgaria). Abstract. We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators of the algebra of invariants. In the Lie case, when the algebra of invariants is not finitely generated, we give a minimal system of generators of the invariants in the commutator [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrod format (in Room 578 of IMI - BAS and online via Zoom) on November 10, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: Transfinite version of the Mittag-Leffler condition for the vanishing of the derived limit will be delivered by Mishel Carelli (Technion – Israel Institute of Technology, Israel). Abstract.We give a necessary and sufficient condition for an inverse sequence  S0 ← S1 ← . . . indexed by natural numbers to have lim¹S = 0. This condition can be treated as a transfinite version of the Mittag-Leffler condition. We consider inverse sequences in the category of abelian groups. We also show that the class of inverse sequences S [...]

The next meeting of the Algebra and Logic Seminar will be held online via Zoom on November 3, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: A Reduction of Temporary Coalitions in Infinite Multiplayer Games will be delivered by Dimitar Guelev (IMI-BAS, Bulgaria). Abstract.We propose a transformation of Concurrent Game Models which enables the reduction of infinite multiplayer games where players can form temporary coalitions to games with no coalitions by extending moves to include the negotiation steps that lead to the formation of coalitions. We adopt conditional promises as the building blocks of negotiation. Temporary coalitions and their agendas arise as the logical consequences of mutual promises. The transformation enables the use of established solution concepts about games with no coalitions for [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrid format (in Room 578 of IMI and online via Zoom) on October 20, 2023 (Friday) at 1:00 pm (UTC+3). A talk on: Prime numbers and random walks in a square grid will be delivered by Alberto Fraile (Czech Technical University in Prague, Czech Republic). Joint work with Osame Kinouchi, Prashant Dwivedi, Roberto Martínez, Theophanes E. Raptis, and Daniel Fernández Abstract. One can argue that prime numbers present perplexing features, in a hybrid of local unpredictability and global regular behavior. It is this interplay between randomness and regularity that motivated searches for both local and global patterns that could potentially become signatures for certain underlying fundamental mathematical properties.In recent years, computer simulations [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrid format (in Room 578 of IMI and online via Zoom) on October 13, 2023 (Friday) at 1:00 pm (UTC+3). A talk on: Emmy Noether’s Theorem on the Finite Generation of the Algebra of Invariants will be delivered by Marin Genov (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract. I will introduce Emmy Noether’s theorem on the finite generation of invariants and give two proofs of it. As an example, I will also calculate the algebra of invariants of the dihedral group of order 2n acting on C[x,y]. Link to the Zoom room: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Algebra and Logic Department, IMI - BAS http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================