My primary research interest is in the interplay between combinatorics and algebraic structures. By employing combinatorial tools such as symmetric functions, partitions, tableaux, graphs, posets, and crystal bases, one can gain significant insight on algebraic and geometric structures such as groups, algebras and rings; and, conversely, the corresponding structure theory can often lead to surp...

To each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category AFF(C)κ of smooth modules (in the sense of Kazhdan and Lusztig [9]) of finite length over the corresponding affine Kac– Moody algebra in the case of central charge less than the critical level. Equivalent characterizations ...

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra. The main results are the classification of the irreducible modules, a version of Steinberg’s Tensor Product Theorem, and the construction of positive characte...

For an associative ring R, let P be an R-module with S = EndR(P). C. Menini and A. Orsatti posed the question of when the related functor HomR(P, −) (with left adjoint P ⊗S −) induces an equivalence between a subcategory of R M closed under factor modules and a subcategory of S M closed under submodules. They observed that this is precisely the case if the unit of the adjunction is an epimorphi...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

Abstract We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that are finite-dimensional, resolving in the affirmative conjecture Witten.

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

fault tolerance is one of the important issues in industries, such as transportation, military, chemical and nuclear sectors. reliability and safety are two vital attributes of fault tolerant systems, and redundancy is a common way to improve these parameters. this article studies the impact of including cold standby spares in system architecture. to do this, it uses the markov model of the sys...

We show that ideal submodules and closed ternary ideals in Hilbert modules are the same. use this insight as a little peg on which to hang note about interrelations with other notions regarding modules. In Section 3, we (and equivalent notions) merit fully, terms of homomorphisms quotients, be called (not necessarily full) The properties checked intrinsically formulated for (without any referen...

Let k be an algebraically closed field, let X be a topological space, let A be a sheaf of associative k-algebras on X, and let F = {F1, . . . ,Fp} be a finite family of sheaves of left A-modules on X. In this paper, we develop a noncommutative deformation theory for the family F . This theory generalizes the noncommutative deformation theory for finite families of left modules over an associati...