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.
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...
We find examples of polynomials whose eigenring is a central simple algebra over the field .
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.
In this paper,we state and prove an analog of Lie product formula in the setting of Euclidean Jordan algebras.