The next meeting of the Algebra and Logic Seminar will be held on February 21, 2025 (Friday) at 1:00 pm (UTC+2). A talk on: Classification of C*-algebras through the lens of Cartan subalgebras will be delivered by Ali Raad (American University in Bulgaria). Abstract.C*-algebras were introduced in the last century following various attempts to mathematically formalize the foundations of quantum mechanics. As such they encapsulate the study of noncommutative topology, as every C*-algebra is an algebra of bounded operators on some Hilbert space. Over the years there has been a significant attempt to classify C*-algebras by an invariant consisting of K-theoretic and tracial data. A recent breakthrough result has shown that every classifiable C*-algebra has a distinguished Abelian subalgebra called a Cartan subalgebra. Cartan subalgebras [...]

The next meeting of the Algebra and Logic Seminar will be held on November 22, 2024 (Friday) at 1:00 pm (UTC+2). A talk on: On Köthe’s normality question for locally finite-dimensional central division algebras will be delivered by Ivan Chipchakov, IMI - BAS. Abstract. This talk considers Köthe's question of whether every associative locally finite-dimensional (abbr., LFD) central division algebra R over a field K is a normally locally finite (abbr., NLF) algebra over K, that is, whether every nonempty finite subset Y of R is contained in a finite-dimensional central K-subalgebra RY of R. It shows that the answer to the posed question is negative if K is a purely transcendental extension of infinite transcendence degree over an algebraically closed field k. On the other hand, central division LFD-algebras [...]

The next meeting of the Algebra and Logic Seminar will be held online via Zoom on April 12, 2024 (Friday) at 1:00 pm (UTC+2). A talk on: On an Aspect of Second Quantum Revolution will be delivered by Valentin Iliev, IMI - BAS. Abstract.The 2022 Nobel Prize in Physics has been awarded to Alain Aspect, John Clauser, and Anton Zeilinger for their work in Quantum Theory. Mass media called this event part of second quantum revolution which includes mainly quantum computing and other super-technologies. Here we discuss Alain Aspect's version of Einstein-Podolsky-Rosen thought experiment and show that there exists an internal dependence of the simultaneous measurements made by the two pairs of linear polarizers operated in each leg of the apparatus during this experiment. [...]

The next meeting of the Algebra and Logic Seminar will be held online via Zoom on April 12, 2024 (Friday) at 1:00 pm (UTC+2). A talk on: On an Aspect of Second Quantum Revolution will be delivered by Valentin Iliev, IMI - BAS. Abstract.The 2022 Nobel Prize in Physics has been awarded to Alain Aspect, John Clauser, and Anton Zeilinger for their work in Quantum Theory. Mass media called this event part of second quantum revolution which includes mainly quantum computing and other super-technologies. Here we discuss Alain Aspect's version of Einstein-Podolsky-Rosen thought experiment and show that there exists an internal dependence of the simultaneous measurements made by the two pairs of linear polarizers operated in each leg of the apparatus during this experiment. [...]

The next meeting of the Algebra and Logic Seminar will be held online via Zoom on March 29, 2024 (Friday) at 1:00 pm (UTC+2). A talk on: Generalized Definability of Discrete Time Interval-based Temporal Connectives will be delivered by Dimitar Guelev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract.In Linear Temporal Logic with past (PLTL), expressive completeness implies that any first-order definable connective is also definable in the temporal language based on the Since and Until temporal operators. This is not the case about discrete time interval-based temporal logics with state-based semantics for the propositional variables. In this talk I prove the next best thing about the extension ITLNL of Moszkowski's discrete time propositional Interval Temporal Logic (ITL) by the neighbourhood modalities: given an interval-based connective # which admits [...]

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, [...]