In this paper some classes of ternary algebraic structures (semi-heaps, heaps) are considered. The connection between heaps (laterally commutative heaps) and corresponding algebraic and geometric structures is presented. The equivalence of heap existence and the Desargues system on the same set is directly proved. It is the starting point for an analogous result about a laterally commutative he...

Kečkić and Lazović introduced an axiomatic approach to Fredholm theory by considering type elements in a unital $$C^{*}$$ -algebra as generalization of -Fredholm operators on the standard Hilbert -module Mishchenko Fomenko properly infinite von Neumann algebra Breuer. In this paper, we establish semi-Fredholm -algebras continuation Lazović. We introduce notion element semi-Weyl -algebra. prove ...

A classical theorem of Veldkamp describes the center an enveloping algebra a Lie semi-simple algebraic group in characteristic p . We generalize this result to class algebras with property that they arise as reduction modulo ≫ 0 from g , such has no nontrivial semi-invariants Sym ( ) and is polynomial algebra. As application, we solve derived isomorphism problem for above algebras.

We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current algebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representat...

Max-times algebra, sometimes known as subtropical algebra, is a semi-ring over the nonnegative real numbers where the addition operation is the max function and the multiplication is the standard one. Factorizing a nonnegative matrix over the maxtimes algebra, instead of the standard (nonnegative) one, allows us to find structures and regularities that cannot be easily expressed in the standard...

I summarize some recent results obtained in collaboration with P. Bouwknegt and K. Pilch on the spectrum of physical states in W 3 gravity coupled to c = 2 matter. In particular, it is shown that the algebra of operators corresponding to physical states – defined as a semi-infinite (or BRST) cohomology of the W 3 algebra – carries the structure of a G-algebra. This G-algebra has a quotient whic...

Let g be a finite-dimensional complex reductive semi simple Lie algebra. We present a new calculation of the continuous cohomology of the Lie algebra zg[[z]]. In particular, we shall give an explicit formula for the Laplacian on the Lie algebra cochains, from which we can deduce that the cohomology in each dimension is a finite-dimensional representation of g which contains any irreducible repr...

Let g be a finite-dimensional complex reductive semi simple Lie algebra. We present a new calculation of the continuous cohomology of the Lie algebra zg[[z]]. In particular, we shall give an explicit formula for the Laplacian on the Lie algebra cochains, from which we can deduce that the cohomology in each dimension is a finite-dimensional representation of g which contains any irreducible repr...

Abstract The generalized Broer-Kaup-Kupershmidt (generalized BKK) isospectral problem, including the x-derivative of potential, is considered based on Lie algebra A1. The variational trace identity is extended to construct Hamiltonian structure of generalized BKK system. The Lie algebra A1 is extended to the non-semi-simple Lie algebra of 4 × 4 matrix form, from which a hierarchy of soliton equ...