Related papers: Affine Algebras with Arbitrary Simple Modules
In this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consists on stratifying systems of infinite size in the module category of an algebra $A$. In the…
Iterated loop algebras are by definition obtained by repeatedly applying the loop construction, familiar from the theory of affine Kac-Moody Lie algebras, to a given base algebra. Our interest in this iterated construction is motivated by…
In this paper we propose a way to construct an analytic space over a non-archimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is motivated by the junction of Homological…
We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…
Some forms of Lie algebras of types E_6, E_7, and E_8 are constructed using the exterior cube of a rank 9 finitely generated projective module.
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…
We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are {\em simple currents} associated with semisimple weight one primary vectors. In the case that the…
We apply the construction of the universal lower-bounded generalized twisted modules by the author to construct universal lower-bounded and grading-restricted generalized twisted modules for affine vertex (operator) algebras. We prove that…
We construct certain integral structures for the cores of reduced tame extended affine Lie algebras of rank at least 2. One of the main tools to achieve this is a generalization of Chevalley automorphisms in the context of extended affine…
It is proved that uniformly bounded simple modules over higher rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules of the intermediate series…
By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra $A_1 ^{(1)}$ of level $-{4/3}$. As an application, we show that the W(2,5) algebra with central…
We construct free cubic implication algebras with finitely many generators, and determine the size of these algebras.
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
We prove a result that can be applied to determine the finite-dimensional simple Poisson modules over a Poisson algebra and apply it to numerous examples. In the discussion of the examples, the emphasis is on the correspondence with the…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…