Related papers: Two vertex geometrically irreducible algebras
We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two…
We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…
A complete classification of two-dimensional algebras over algebraically closed fields is provided
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
Possible irreducible holonomy algebras $\g\subset\sp(2m,\Real)$ of odd Riemannian supermanifolds and irreducible subalgebras $\g\subset\gl(n,\Real)$ with non-trivial first skew-symmetric prolongations are classified. An approach to the…
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
In this paper, all irreducible weight modules with finite dimensional weight spaces over the twisted Heisenberg-Virasoro algebra are determined. There are two different classes of them. One class is formed by simple modules of intermediate…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We first investigate the algebraic structure of vertex algebroids $B$ when $B$ are simple Leibniz algebras. Next, we use these vertex algebroids $B$ to construct indecomposable non-simple $C_2$-cofinite $\mathbb{N}$-graded vertex algebras…
We give a geometric classification of complex $n$-dimensional $2$-step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible components and their dimensions. As a corollary, we have a…
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
We classify the finite dimensional irreducible representations of affine Hecke algebras of type B_2 with unequal parameters.
We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.