A computer-based approach to the classification of nilpotent Lie algebras.
A concrete analysis of the radical concept.
A conjecture on Lie algebras admitting a regular automorphism of finite order
A construction for algebras satisfying the maximal condition for subalgebras
A Construction of Representations of Weyl Groups.
A construction of some ideals in affine vertex algebras.
A constructive method to determine the variety of filiform Lie algebras
In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also computed explicitly these polynomials in the case of dimensions 11 and 12.
A criterion for the minimal closedness of the Lie subalgebra corresponding to a connected nonclosed Lie subgroup.
A description of discrete series using step algebras.
A family of regular vertex operator algebras with two generators
For every m ∈ ℂ ∖ 0, −2 and every nonnegative integer k we define the vertex operator (super)algebra D m,k having two generators and rank . If m is a positive integer then D m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.
A family of tridiagonal pairs related to the quantum affine algebra .
A formula for the logarithm of the KZ associator.
A Frobenius formula for the characters of the Hecke algebras.
A general approach to finite-dimensional division algebras
We present a short and rather self-contained introduction to the theory of finite-dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In Sections 2-3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories 𝒟ₙ(k), and the role played by the irreducible...
A generalisation of Amitsur's A-polynomials
We find examples of polynomials whose eigenring is a central simple algebra over the field .
A generalization of the Enright-Varadarajan modules
A Generalized Hecke Identity.
A Generalized ...-Invariant for the Primitive Spectrum of a Semisimple Lie Algebra.
A Geometric Realization of
A glimpse at the theory of Jordan-Banach triple systems.
In this article, a survey of the theory of Jordan-Banach triple systems is presented. Most of the recent relevant results in this area have been included, though no proofs are given.